Why X-Rays and Gamma Rays Can Overlap in Energy

X-rays and gamma rays can have almost identical photon energies despite being produced by different processes. Learn why their energy ranges overlap, how their wavelengths compare, and why photon energy and photon count must be treated separately.

A tungsten target can emit an X-ray photon with an energy of 59.319 keV. An excited nucleus of neptunium-237 can emit a gamma-ray photon with an energy of 59.537 keV.

These energies differ by less than 0.4%. Yet one photon is classified as an X-ray and the other as a gamma ray.

How can that happen?

X-rays and gamma rays are distinguished primarily by how they are produced, not by a fixed boundary in photon energy. X-rays are associated with electron interactions outside the nucleus, while gamma rays are associated with transitions within the nucleus. Both processes can release photons with very similar energies.

Before going further, consider this: if you were given a single photon with an energy of 59.4 keV, could you tell whether it was an X-ray or a gamma ray?

No. Its energy alone would not tell you where it came from.

01The historical clue: two different sources of radiation

The distinction between X-rays and gamma rays developed through experiments involving two different sources.

The important discovery was not that one type of radiation had a particular energy. It was that similar penetrating radiation could be produced by different physical processes.

How Röntgen discovered X-rays

In 1895, Wilhelm Röntgen was investigating electrical discharges in a device called a Crookes tube.

The apparatus consisted of an evacuated glass tube containing a negative electrode (cathode) and a positive electrode (anode). When a high voltage was applied, electrons travelled across the tube and struck the glass.

Outside the tube, Röntgen placed a fluorescent screen coated with a substance called barium platinocyanide.

What should have happened if ordinary visible light was escaping from the tube?

The thick black cardboard should have blocked it. Cathode rays, which are streams of electrons, also could not travel through the glass and across the room to the screen.

Instead, the fluorescent screen continued to glow.

Röntgen realised that an unknown form of radiation was escaping from the tube and passing through the cardboard.

Further experiments showed that the radiation could pass through soft tissue while being absorbed more strongly by bones and metals. Photographic plates recorded these differences, including the now-famous image of the bones and ring in his wife’s hand.

Röntgen called the radiation X-rays because its nature was initially unknown.

The American Physical Society provides a detailed historical account of Röntgen’s discovery of X-rays.

Where gamma rays entered the picture

Scientists were also investigating radiation emitted by radioactive substances.

In 1900, Paul Villard identified a third component of radiation from radioactive materials. Following the naming convention associated with Rutherford’s earlier alpha and beta classifications, this became known as gamma radiation.

An important question remained: were gamma rays actually electromagnetic waves, like X-rays?

In 1914, Ernest Rutherford and Edward Andrade demonstrated the wave nature of gamma rays using diffraction experiments.

This established that gamma rays and X-rays belonged to the same broad family of electromagnetic radiation.

NASA’s history of gamma-ray astronomy records these developments.

The historical distinction eventually became clear: the two types of radiation could have the same fundamental electromagnetic properties while being produced by different processes.

02How X-rays and gamma rays are produced

To understand why their energies overlap, we need to look at where the energy comes from.

X-rays: energy released by electrons

X-rays are commonly produced through two processes involving electrons.

The first is called bremsstrahlung, which means braking radiation.

Imagine an electron travelling towards a tungsten target inside an X-ray tube.

The electron has kinetic energy because it is moving. As it passes close to a positively charged nucleus in the target, the electric force changes its motion. It slows down or changes direction.

The electron loses kinetic energy, and some of this energy can be emitted as an X-ray photon.

The energy of the emitted photon depends on how much kinetic energy the electron loses.

This produces a continuous range of possible X-ray energies.

There is a maximum possible photon energy. If an electron transfers all its kinetic energy to a single photon, then:

\[ E_{\text{max}}=eV \]

where:

  • \(E_{\text{max}}\) is the maximum photon energy,
  • \(e\) is the magnitude of the electron’s charge,
  • \(V\) is the accelerating potential difference.

For example, an electron accelerated through 100 kV gains 100 keV of kinetic energy.

A bremsstrahlung photon can therefore have an energy approaching 100 keV, although most photons have less energy.

The second process produces characteristic X-rays.

Suppose an incoming electron knocks an electron out of an inner shell of a tungsten atom. This leaves a vacancy.

An electron from a higher-energy shell can fall into the vacancy. The difference in the electron’s energy is released as an X-ray photon.

\[ E_\gamma=E_{\text{initial}}-E_{\text{final}} \]

The energy of this photon depends on the atomic electron energy levels.

Different elements have different electron energy levels, so they produce characteristic X-ray energies.

Notice something important: neither process requires a change to the atomic nucleus.

The X-rays originate from interactions involving electrons outside the nucleus.

The Australian Radiation Protection and Nuclear Safety Agency (ARPANSA) explains both production mechanisms in its X-ray reference guide.

Gamma rays: energy released by the nucleus

Gamma rays are produced when an excited atomic nucleus loses energy.

A nucleus can become excited following radioactive decay or a nuclear reaction. It then moves from a higher nuclear energy state to a lower one.

The energy difference is emitted as a gamma-ray photon.

\[ E_\gamma=E_i-E_f \]

Here:

  • \(E_i\) is the initial nuclear energy,
  • \(E_f\) is the final nuclear energy,
  • \(E_\gamma\) is the emitted photon energy.

The photon carries away the energy released by the nucleus.

For more detail about the nuclear process, see tutorgum’s Gamma Decay Explained: Emission, Penetration and Ionisation.

We now have two different processes:

X-raysGamma rays
Produced by electron interactions outside the nucleusProduced by transitions within the nucleus
Can result from electron decelerationResult from nuclear de-excitation
Can result from electron-shell transitionsResult from nuclear energy-level transitions
Can have continuous or discrete energy spectraTypically have discrete nuclear transition energies

Both produce electromagnetic photons.

The important point is that the energy of a photon depends on the energy released during its production, not simply on whether the source is an atom or a nucleus.

03Why their energy ranges overlap

Here is the central idea.

An emitted photon carries away an amount of energy equal to the energy released by its source.

Different physical systems can release the same amount of energy.

Think of two staircases in different buildings. One staircase might belong to a house, while the other belongs to a school. If both have a step with the same vertical height, a ball falling down either step can lose the same gravitational potential energy.

The buildings are different, but the energy change is the same.

In a similar way, an electron transition and a nuclear transition can release almost identical amounts of energy.

The analogy is not exact: atomic and nuclear energy levels are quantum states, not literal steps. However, it captures the important relationship between the size of an energy change and the energy of the emitted photon.

A real example: almost identical photon energies

Consider these two experimentally established reference energies.

SourceRadiationPhoton energy
Tungsten Kα1 electron-shell transitionX-ray59.318847 keV
Neptunium-237 nuclear transition following americium-241 decayGamma ray59.537 keV

The tungsten value is listed in the NIST X-ray transition database. The americium-241 gamma-ray energy is listed in IAEA nuclear data.

The difference is only:

\[ \Delta E=59.537-59.318847 \]

\[ \Delta E=0.218153\text{ keV} \]

That is approximately 0.37% of their mean energy.

These photons have different origins, but their energies are extremely close.

Their wavelengths are almost identical too

Remember the relationship between photon energy and wavelength:

\[ E=\frac{hc}{\lambda} \]

Rearranging:

\[ \lambda=\frac{hc}{E} \]

where:

  • \(E\) is photon energy in joules,
  • \(h=6.626\times10^{-34}\text{ J s}\) is Planck’s constant,
  • \(c=3.00\times10^8\text{ m s}^{-1}\) is the speed of light in a vacuum,
  • \(\lambda\) is wavelength in metres.

Using the convenient conversion \(hc\approx1.23984\text{ keV nm}\):

For the tungsten X-ray:

\[ \lambda_X=\frac{1.23984}{59.318847} \]

\[ \lambda_X\approx0.02090\text{ nm} \]

For the gamma ray:

\[ \lambda_\gamma=\frac{1.23984}{59.537} \]

\[ \lambda_\gamma\approx0.02082\text{ nm} \]

Both wavelengths are approximately 21 picometres.

This is another way to see why energy cannot be used as a definitive classification method.

Why the old energy ranking fails

You might have seen electromagnetic spectrum diagrams that suggest gamma rays always have higher energies than X-rays.

This is a useful simplification when describing many familiar radiation sources, but it is not a universal rule.

There are two reasons it fails.

First, some nuclear transitions release relatively small amounts of energy.

The 59.537 keV gamma-ray transition from neptunium-237 is one example.

Second, electron interactions can produce extremely energetic X-rays.

An electron accelerated to several mega-electronvolts can produce bremsstrahlung X-rays with photon energies reaching the MeV range.

For example, accelerator-based radiotherapy can use X-rays with energies of several MeV.

The energy ranges therefore overlap considerably.

The correct distinction is the production mechanism, not an assumed ranking of photon energies.

04Photon energy and photon count are two different things

There is another distinction worth getting right.

A beam containing more photons does not necessarily contain photons with more energy.

Consider two beams:

  • Beam A contains 1,000 photons, each carrying 50 keV.
  • Beam B contains 100 photons, each carrying 50 keV.

Which beam has more energy?

Beam A.

But each individual photon carries exactly the same energy in both beams.

The total energy depends on two quantities:

  1. The energy carried by each photon.
  2. The number of photons present.

Mathematically:

\[ E_{\text{total}}=NE_\gamma \]

where:

  • \(E_{\text{total}}\) is the total energy,
  • \(N\) is the number of photons,
  • \(E_\gamma\) is the energy per photon.

If we consider how much energy arrives each second, we can calculate power:

\[ P=\dot{N}E_\gamma \]

Here, \(\dot{N}\) is the photon emission or arrival rate, measured in photons per second.

This distinction is important when interpreting radiation intensity.

A beam can become more intense because it contains more photons per second, without any increase in the energy of each photon.

A detector measures energy and count separately

An energy-resolving detector can record two different things:

  • The energy deposited by individual photons.
  • The number of detected photons within a particular energy range.

The first determines where a peak appears on an energy spectrum.

The second determines how many counts contribute to that peak.

A higher peak does not automatically mean higher-energy photons. It may simply mean more photons were detected.

There is also a practical limitation: detector efficiency, source distance, geometry, and absorption can affect the measured count rate. A detector’s count rate is not automatically equal to the total emission rate of the source.

This distinction becomes particularly important when comparing an X-ray tube with a radioactive gamma-ray source.

05How wavelength connects to real applications

Although the labels X-ray and gamma ray do not establish a fixed energy ranking, wavelength still matters.

Since

\[ E=\frac{hc}{\lambda} \]

higher-energy photons have shorter wavelengths.

This relationship helps explain why different parts of the X-ray and gamma-ray ranges are useful for different applications.

ApplicationApproximate photon energyApproximate wavelengthWhy it is useful
X-ray crystallography8-17 keV0.155-0.073 nmWavelengths are comparable to atomic spacings, allowing diffraction patterns to reveal crystal structure.
Diagnostic X-ray imaging20-60 keV0.062-0.021 nmX-rays penetrate tissue, with different absorption by different materials producing image contrast.
Cobalt-60 gamma irradiation1.17-1.33 MeV1.06-0.93 pmHighly penetrating photons can be used for industrial irradiation and sterilisation.
Accelerator-based X-ray radiotherapy3-10 MeV0.41-0.12 pmHigh-energy bremsstrahlung X-rays can deliver radiation into deeper regions of the body.

These are representative values, not boundaries separating X-rays from gamma rays. The application ranges and production methods are described in ARPANSA’s X-ray information and the IAEA’s information on cobalt-60 irradiation.

There are two different ideas operating here.

For crystallography, wavelength is especially important because it determines the diffraction geometry. X-ray wavelengths are comparable to the distances between atomic planes in crystals.

For medical imaging and radiation therapy, photon energy is particularly important because it affects how radiation interacts with tissue and how deeply it can penetrate.

The number of photons also matters because it affects the intensity of the beam and the amount of energy delivered over time.

So wavelength, photon energy, and photon count each tell us something different.

For additional practice with energy-wavelength conversions, see tutorgum’s How to Convert Photon Energy (eV) into Wavelength.

06Worked examples

Worked example: Comparing an X-ray and gamma-ray photon

A tungsten target produces a characteristic X-ray photon with an energy of 59.318847 keV. An excited neptunium-237 nucleus produces a gamma-ray photon with an energy of 59.537 keV.

Calculate the wavelength of each photon and determine the percentage difference between their energies.

Step 1

\[ \lambda=\frac{hc}{E} \]

Using convenient units:

\[ hc=1.23984\text{ keV nm} \]

Step 2

\[ \lambda_X=\frac{1.23984}{59.318847} \]

\[ \lambda_X=0.02090\text{ nm} \]

Step 3

\[ \lambda_\gamma=\frac{1.23984}{59.537} \]

\[ \lambda_\gamma=0.02082\text{ nm} \]

Step 4

First, find the difference:

\[ \Delta E=59.537-59.318847 \]

\[ \Delta E=0.218153\text{ keV} \]

Using the mean energy as the reference:

\[ \%\text{ difference} = \frac{0.218153}{59.4279235}\times100 \]

\[ \boxed{0.37\%} \]

The two photons have almost identical energies and wavelengths despite having different origins.

This demonstrates why wavelength and energy cannot independently identify whether radiation is an X-ray or a gamma ray.

Worked example: Comparing photon number and beam power

Two radiation sources produce photons with an energy of 59.5 keV.

At a particular detector position:

  • Source A delivers \(2.0\times10^6\) photons per second.
  • Source B delivers \(1.0\times10^4\) photons per second.

Calculate the power delivered by each beam at that position.

Assume the stated rates represent photons arriving at the detector, with no losses.

Step 1

First, convert kiloelectronvolts into electronvolts:

\[ 59.5\text{ keV}=59.5\times10^3\text{ eV} \]

Using \(1\text{ eV}=1.602\times10^{-19}\text{ J}\):

\[ E_\gamma=59.5\times10^3 \times1.602\times10^{-19} \]

\[ E_\gamma=9.53\times10^{-15}\text{ J} \]

Step 2

Use:

\[ P=\dot{N}E_\gamma \]

Substitute:

\[ P_A=2.0\times10^6 \times9.53\times10^{-15} \]

\[ \boxed{P_A=1.91\times10^{-8}\text{ W}} \]

Step 3

\[ P_B=1.0\times10^4 \times9.53\times10^{-15} \]

\[ \boxed{P_B=9.53\times10^{-11}\text{ W}} \]

Step 4

\[ \frac{P_A}{P_B} = \frac{2.0\times10^6}{1.0\times10^4} \]

\[ \boxed{\frac{P_A}{P_B}=200} \]

Source A delivers 200 times more energy per second than Source B.

However, every photon from both sources still has an energy of 59.5 keV.

The difference comes entirely from the number of photons arriving each second, not the energy of each photon.

07A reliable decision rule for exams

When comparing X-rays and gamma rays, separate the information you are given.

Information providedWhat you can conclude
Electrons decelerate in a targetX-rays are produced.
An electron moves between atomic energy levelsCharacteristic X-rays can be produced.
An excited nucleus loses energyGamma rays are produced.
Photon energy is givenYou can calculate frequency and wavelength, but cannot determine the radiation’s origin from energy alone.
Wavelength is givenYou can calculate photon energy, but cannot determine its origin from wavelength alone.
Photon count or count rate is givenYou can investigate total energy and power, but cannot determine the radiation type from count rate alone.
A detector records a peak at a particular energyYou know the detected photon energy, subject to detector resolution, but not necessarily the source mechanism.

A particularly tempting misconception is that gamma rays must always have greater photon energy than X-rays.

Remember that this is not a reliable classification rule.

For HSC-style explanations, focus on the production mechanism:

  • X-rays: electron interactions outside the nucleus.
  • Gamma rays: nuclear transitions.

Both are electromagnetic photons and both travel at the speed of light in a vacuum.

08Questions and solutions

The following questions progress from standard photon calculations to more challenging problems involving energy spectra, source identification, and photon count.

Question 1

A monochromatic electromagnetic beam contains photons with a wavelength of \(0.0250\text{ nm}\).

(a) Calculate the energy of one photon in keV.

(b) Can this energy alone establish whether the beam consists of X-rays or gamma rays? Explain.

Solution 1

The photon energy is 49.6 keV, and this value alone cannot establish whether the radiation is X-rays or gamma rays.

Step 1: Write the energy-wavelength relationship.

\[ E=\frac{hc}{\lambda} \]

Using \(hc=1.23984\text{ keV nm}\):

Step 2: Substitute the wavelength.

\[ E=\frac{1.23984}{0.0250} \]

\[ \boxed{E=49.6\text{ keV}} \]

Step 3: Explain the classification.

The calculated energy tells us how much energy each photon carries.

However, an electron-shell transition and a nuclear transition can both release approximately 49.6 keV.

Therefore, the photon energy does not reveal the production mechanism.

To distinguish the two, we need information about the source.

Question 2

An X-ray tube accelerates electrons through a potential difference of 85.0 kV before they strike a tungsten target.

Assume that an electron can transfer all its kinetic energy to a single bremsstrahlung photon.

(a) Calculate the maximum possible energy of an X-ray photon in keV.

(b) Calculate the minimum possible wavelength of the bremsstrahlung radiation.

(c) An excited nucleus also produces a gamma-ray photon with an energy of 85.0 keV. Compare the two photons and explain why they have different classifications.

Solution 2

The maximum X-ray photon energy is 85.0 keV, and its minimum wavelength is approximately \(1.46\times10^{-11}\text{ m}\). The gamma-ray photon can have exactly the same energy and wavelength.

Step 1: Calculate the maximum electron kinetic energy.

The energy gained by an electron accelerated through a potential difference is:

\[ E_{\text{kinetic}}=eV \]

An electron gains 1 eV of energy when accelerated through 1 V.

Therefore:

\[ E_{\text{max}}=85.0\text{ keV} \]

This is the maximum possible bremsstrahlung photon energy because we have assumed that all the electron’s kinetic energy is transferred to one photon.

Step 2: Calculate the minimum wavelength.

\[ \lambda_{\min}=\frac{hc}{E_{\text{max}}} \]

Substitute:

\[ \lambda_{\min}=\frac{1.23984}{85.0} \]

\[ \lambda_{\min}=0.014586\text{ nm} \]

Convert to metres:

\[ \boxed{\lambda_{\min}=1.46\times10^{-11}\text{ m}} \]

Step 3: Compare the X-ray and gamma-ray photons.

Both photons have an energy of 85.0 keV.

Therefore, both have the same frequency and wavelength.

However, the X-ray photon was produced by an electron losing kinetic energy in the tungsten target.

The gamma-ray photon was produced by a nuclear energy-level transition.

The production mechanisms are different, even though the resulting photons have identical energy.

Question 3

A tungsten X-ray tube operates at an accelerating potential of 90 kV.

Its spectrum contains a characteristic Kα1 X-ray line with an energy of 59.319 keV.

The binding energy of an electron in tungsten’s K shell is approximately 69.5 keV.

The tube voltage is changed in two stages:

  • First, it is increased from 90 kV to 110 kV.
  • Then, it is reduced from 110 kV to 65 kV.

Predict what happens to:

(a) The maximum energy of the bremsstrahlung spectrum when the voltage increases.

(b) The energy of the characteristic Kα1 line when the voltage increases.

(c) The characteristic Kα1 line when the voltage is reduced to 65 kV.

(d) The possibility of producing bremsstrahlung photons with energies close to 59.3 keV at 65 kV.

Solution 3

Increasing the voltage moves the bremsstrahlung endpoint to a higher energy but does not change the characteristic line energy. Reducing the voltage below the K-shell binding energy removes the Kα1 line, although bremsstrahlung photons near 59.3 keV can still be produced.

Step 1: Consider the bremsstrahlung endpoint.

The maximum photon energy is:

\[ E_{\text{max}}=eV \]

At 90 kV:

\[ E_{\text{max}}=90\text{ keV} \]

At 110 kV:

\[ E_{\text{max}}=110\text{ keV} \]

Therefore, the continuous spectrum extends to a higher maximum energy.

Step 2: Consider the characteristic X-ray energy.

The Kα1 photon is produced when an electron from the L3 shell fills a vacancy in the K shell.

Its energy is determined by the difference between the two atomic energy levels.

Changing the accelerating voltage does not change these energy levels.

Therefore, the Kα1 photon energy remains:

\[ \boxed{E_{K\alpha1}=59.319\text{ keV}} \]

The number of photons in the line may change, but its characteristic energy remains fixed.

Step 3: Consider reducing the voltage to 65 kV.

An electron accelerated through 65 kV gains 65 keV of kinetic energy.

However, the tungsten K-shell binding energy is approximately 69.5 keV.

The incoming electron therefore does not have enough energy to remove a K-shell electron.

Without a K-shell vacancy, the characteristic Kα1 transition cannot occur.

The narrow Kα1 line disappears.

Step 4: Consider bremsstrahlung photons.

This is the subtle part.

The maximum bremsstrahlung photon energy at 65 kV is 65 keV.

Therefore, photons with energies around 59.3 keV are still possible.

However, these photons would be part of the continuous bremsstrahlung spectrum, not the characteristic Kα1 line.

The distinction is between the energy required to create a particular electron-shell vacancy and the energy of a photon that can be produced through electron deceleration.

Question 4

An accelerator-based radiotherapy system produces bremsstrahlung X-rays, including photons with an energy of 6.0 MeV.

A separate cobalt-60 source emits gamma rays, including photons with an energy of 1.33 MeV.

(a) Calculate the wavelength of each photon in metres.

(b) Determine which photon has the greater energy.

(c) Explain why the result does not contradict the distinction between X-rays and gamma rays.

Solution 4

The 6.0 MeV X-ray photon has approximately 4.51 times the energy of the 1.33 MeV gamma-ray photon. It also has a shorter wavelength. This does not contradict their classifications because their names describe their production mechanisms.

Step 1: Calculate the X-ray wavelength.

Convert the energy into keV:

\[ 6.0\text{ MeV}=6000\text{ keV} \]

Use:

\[ \lambda=\frac{hc}{E} \]

\[ \lambda_X=\frac{1.23984}{6000} \]

\[ \lambda_X=0.00020664\text{ nm} \]

Converting to metres:

\[ \boxed{\lambda_X=2.07\times10^{-13}\text{ m}} \]

Step 2: Calculate the gamma-ray wavelength.

Convert:

\[ 1.33\text{ MeV}=1330\text{ keV} \]

Substitute:

\[ \lambda_\gamma=\frac{1.23984}{1330} \]

\[ \boxed{\lambda_\gamma=9.32\times10^{-13}\text{ m}} \]

Step 3: Compare photon energies.

\[ \frac{E_X}{E_\gamma}=\frac{6.0}{1.33} \]

\[ \boxed{\frac{E_X}{E_\gamma}=4.51} \]

The X-ray photon has approximately 4.51 times the energy of the gamma-ray photon.

It also has a wavelength approximately 4.51 times shorter.

Step 4: Explain the classification.

The accelerator-generated X-ray is produced when high-energy electrons interact with a target and lose kinetic energy.

The cobalt-60 gamma ray is produced through a nuclear transition.

Therefore, the X-ray can have greater energy than the gamma ray without contradicting the definitions.

This is a useful example because it directly disproves the assumption that gamma rays must always have greater energy.

Question 5

A physics laboratory investigates two radiation sources using an energy-resolving detector.

The sources are:

  • Source A: a tungsten-target X-ray tube.
  • Source B: an americium-241 radioactive source.

The tungsten source produces a characteristic Kα1 X-ray at 59.319 keV. The americium-241 source produces a gamma-ray photon at 59.537 keV.

The detector has an energy resolution of 0.50 keV. Consequently, it cannot resolve the two closely spaced lines, and they appear as one combined peak.

The experiment is conducted as follows:

Initial measurement

The X-ray tube operates at 90.0 kV. After subtracting the smooth bremsstrahlung background, the combined narrow-peak photon rate is:

\[ \dot N_{\text{initial}}=1.00\times10^3 \text{ photons s}^{-1} \]

Second measurement

The X-ray tube voltage is reduced to 60.0 kV. The americium-241 source, detector position, and geometry remain unchanged.

The measured narrow-peak photon rate becomes:

\[ \dot N_{\text{final}}=2.50\times10^2 \text{ photons s}^{-1} \]

For this question, assume:

  • The tungsten K-shell binding energy is 69.5 keV.
  • The americium-241 gamma emission rate remains constant.
  • Detector efficiency has already been accounted for, so the quoted rates represent photons arriving at the detector.
  • The smooth bremsstrahlung background has been subtracted.
  • There are no other narrow spectral lines in this energy region.
  • The only tungsten narrow line being considered is the Kα1 line.

(a) Explain why the detector cannot distinguish the two original lines using their measured energies.

(b) Determine the original photon rate contributed by each source.

(c) Calculate the power carried by each source’s narrow-line photons before the voltage is reduced.

(d) Explain why reducing the X-ray tube voltage identifies the contributions from the two sources, even though their photon energies are almost identical.

(e) A student argues that the tungsten source must still produce its characteristic Kα1 line at 60 kV because 60 keV is greater than 59.319 keV. Explain the error in this reasoning.

Solution 5

The original narrow peak contains 750 photons per second from the tungsten X-ray source and 250 photons per second from the americium-241 gamma source. Reducing the tube voltage removes the tungsten characteristic line but leaves the gamma-ray contribution unchanged.

Step 1: Determine whether the detector can resolve the two lines.

The energy difference is:

\[ \Delta E=59.537-59.319 \]

\[ \Delta E=0.218\text{ keV} \]

The detector resolution is 0.50 keV.

Since:

\[ 0.218<0.50 \]

the two lines cannot be resolved by this detector.

They appear as one combined peak.

This means the initial energy measurement cannot independently identify the contributions from the two sources.

Step 2: Determine the gamma-ray contribution.

When the tube voltage is reduced to 60 kV, the tungsten electrons no longer have sufficient energy to create K-shell vacancies.

The characteristic Kα1 line therefore disappears.

The americium-241 source is unchanged, so its gamma-ray contribution remains constant.

The final measured narrow-peak rate must therefore be the gamma-ray rate:

\[ \boxed{\dot N_\gamma=250\text{ photons s}^{-1}} \]

Step 3: Calculate the original X-ray contribution.

Initially, both sources contributed to the combined peak.

Therefore:

\[ \dot N_{\text{initial}} = \dot N_X+\dot N_\gamma \]

Rearrange:

\[ \dot N_X = \dot N_{\text{initial}}-\dot N_\gamma \]

Substitute:

\[ \dot N_X=1000-250 \]

\[ \boxed{\dot N_X=750\text{ photons s}^{-1}} \]

The original contributions were:

  • Tungsten X-rays: 750 photons/s.
  • Americium-241 gamma rays: 250 photons/s.

Step 4: Calculate the energy of each photon in joules.

For the power calculation, approximate both photon energies as 59.4 keV.

Convert to joules:

\[ E_\gamma=59.4\times10^3 \times1.602\times10^{-19} \]

\[ E_\gamma=9.52\times10^{-15}\text{ J} \]

Step 5: Calculate the original X-ray power.

Use:

\[ P_X=\dot N_XE_\gamma \]

Substitute:

\[ P_X=750\times9.52\times10^{-15} \]

\[ \boxed{P_X=7.14\times10^{-12}\text{ W}} \]

Step 6: Calculate the gamma-ray power.

\[ P_\gamma=\dot N_\gamma E_\gamma \]

\[ P_\gamma=250\times9.52\times10^{-15} \]

\[ \boxed{P_\gamma=2.38\times10^{-12}\text{ W}} \]

The original total narrow-line power is:

\[ P_{\text{total}}=P_X+P_\gamma \]

\[ P_{\text{total}} = 7.14\times10^{-12} + 2.38\times10^{-12} \]

\[ \boxed{P_{\text{total}}=9.52\times10^{-12}\text{ W}} \]

After reducing the tube voltage, only the narrow gamma-ray line remains.

Its power is:

\[ \boxed{P_{\text{final}}=2.38\times10^{-12}\text{ W}} \]

These values describe the narrow spectral feature, not the entire X-ray tube output.

Step 7: Explain why changing the tube voltage works.

The original detector measurement could not distinguish the two sources because their photon energies were separated by less than the detector’s resolution.

However, changing the tube voltage changes the conditions under which X-rays are produced.

At 90 kV, the incoming electrons have enough kinetic energy to remove tungsten K-shell electrons because:

\[ 90\text{ keV}>69.5\text{ keV} \]

At 60 kV:

\[ 60\text{ keV}<69.5\text{ keV} \]

The electrons can no longer create K-shell vacancies.

Consequently, the characteristic Kα1 line disappears.

The nuclear transition responsible for the americium-241 gamma ray is unaffected by changing the X-ray tube voltage.

The experiment therefore identifies the source contributions by changing one production mechanism while leaving the other unchanged.

Step 8: Identify the student’s mistake.

The student has confused two different energy requirements.

The 59.319 keV value is the energy released when an electron falls from the L3 shell into a K-shell vacancy.

The 69.5 keV value is approximately the energy required to remove a K-shell electron in the first place.

These are not the same energy.

At 60 kV, the tube can still produce bremsstrahlung photons with energies approaching 60 keV. Therefore, photons close to 59.3 keV may still occur in the continuous spectrum.

However, the tube cannot produce the characteristic Kα1 line because it cannot create the necessary K-shell vacancy.

This is the key distinction: a photon having enough energy to be emitted through one process does not mean the source has enough energy to initiate a different process.

The experiment demonstrates something important about radiation measurements. A photon spectrum provides information about energy and photon number, but identifying the production mechanism may require additional evidence about the source and how it responds to controlled changes.

09What to take into the next topic

Keep three quantities separate whenever you analyse electromagnetic radiation:

  • Photon energy tells you how much energy one photon carries.
  • Photon wavelength is inversely related to its energy.
  • Photon count tells you how many photons are present or arrive each second.

None of these quantities alone establishes whether a photon is an X-ray or a gamma ray.

That distinction comes from its production mechanism.

The next useful concept is how these photons interact with matter. The photoelectric effect, Compton scattering, and pair production explain how photon energy is transferred to electrons and other particles.

Those interactions depend on photon energy and the material involved, not simply on whether the incoming photon is labelled an X-ray or a gamma ray.