22.3.3 Gamma Decay

What is Gamma Decay?

Gamma ($\gamma$) decay is the emission of high-energy electromagnetic radiation (gamma photons) from an excited nucleus as it transitions to a lower energy state. Unlike alpha and beta decay, gamma decay involves no change in the atomic number ($Z$) or mass number ($A$) of the nucleus.

General Nuclear Equation

${}_Z^A{X}^{\ast }{\to }_Z^{A}X+\gamma$

where the asterisk (${}^{\ast }$) denotes the nucleus in an excited (metastable) state.

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Why Does Gamma Decay Occur?

After alpha ($\alpha$) or beta ($\beta$) decay, the daughter nucleus is often left in an excited state with excess energy above its ground state. The nucleus releases this excess energy by emitting a gamma photon:

$E_{\gamma }=hf=E_{excited}-E_{ground}$

The nucleus does not change its identity — it is the same nuclide, simply moving from a higher to a lower energy level (analogous to electron transitions in atoms, but at much higher energies).

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Properties of Gamma Radiation

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Change in Atomic Number and Mass Number

Since gamma photons carry no charge and no mass, the parent and daughter nuclei are the same nuclide:

• $\Delta Z=0$
• $\Delta A=0$

Example: Cobalt-60 after beta decay is left in an excited state and undergoes gamma decay:

${}_{27}^{60}{\text{Co}}^{\ast }{\to }_{27}^{60}\text{Co}+\gamma$

The emitted gamma photons have energies of 1.17 MeV and 1.33 MeV — these are used in radiotherapy to treat cancer.

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Energy Calculation in Gamma Decay

The energy of the emitted gamma photon equals the energy difference between the excited and ground states:

$E_{\gamma }=hf=E^{\ast }-E_0$

Worked Example:

A nucleus de-excites from a state 2.50 MeV above the ground state. Find the frequency of the emitted gamma photon.

$E_{\gamma }=2.50\text{ MeV}=2.50\times 10^6\times 1.6\times 10^{-19}\text{ J}=4.0\times 10^{-13}\text{ J}$

$f=\frac{E_{\gamma }}{h}=\frac{4.0\times 10^{-13}}{6.63\times 10^{-34}}\approx 6.03\times 10^{20}\text{ Hz}$

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Spontaneous and Random Nature

Gamma decay, like all radioactive decay, is:

• Spontaneous — it occurs without any external trigger; no external conditions (temperature, pressure, chemical state) can initiate or prevent it.
• Random — it is impossible to predict which specific excited nucleus will decay at any given moment; only the probability of decay per unit time (the decay constant $\lambda$) can be stated.

This means gamma emission following alpha or beta decay is also spontaneous and random — we cannot predict when the excited daughter nucleus will emit its gamma photon.

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