Electron Capture Decay

Electron capture (EC) is a type of radioactive decay that occurs when an atomic electron is captured by a proton in the nucleus. This leads to a transformation of the proton into a neutron and the emission of an electron neutrino (ν_e). The atomic number of the atom decreases by one, but the atomic mass number remains unchanged. Electron capture is similar to β⁺ decay, where a proton is converted into a neutron.

The general equation for electron capture decay is:

$$ Z_D = Z_P - 1 $$

$$ A_D = A_P $$

$$ P + e^- \rightarrow D + \nu_e $$

Where:

P is the parent nucleus.
D is the daughter nucleus after electron capture.
Z_P and Z_D are the atomic numbers of the parent and daughter nuclei, respectively.
A_P and A_D are the mass numbers, which remain unchanged during electron capture.
e^- represents the captured electron.
ν_e is the emitted electron neutrino.

Example of Electron Capture Decay

A well-known example of electron capture decay is the decay of iodine-125 (¹²⁵I), which decays into an excited state of tellurium-125 (¹²⁵Te) through electron capture. The excited tellurium-125 then decays to its ground state via γ decay and internal conversion:

$$ ^{125}_53I + e^- \rightarrow ^{125}_52Te^* + \nu_e $$

In this example:

I¹²⁵ is the parent nucleus (iodine-125) undergoing electron capture.
Te¹²⁵ is the daughter nucleus (tellurium-125), initially in an excited state.
An electron (e^-) is captured, and an electron neutrino (ν_e) is emitted during the process.

Electron Capture and Its Impact on the Atomic Structure

Electron capture has a notable effect on the atom’s structure. After a proton captures an electron, the proton is transformed into a neutron. This decreases the atomic number of the element by one, resulting in a different element. The mass number, however, remains the same because the number of nucleons (protons and neutrons) remains unchanged.

Electron capture typically occurs in heavier elements, especially those that are proton-rich and unstable. It is commonly observed in isotopes of elements like iodine, palladium, and bismuth.

Half-life of Electron Capture

The half-life of electron capture is the time it takes for half of the atoms in a sample of a radioactive substance to undergo electron capture. The decay follows an exponential decay law, similar to other radioactive decay processes. The decay law is given by:

$$ N(t) = N_0 e^{-\lambda t} $$

Where:

N(t) is the number of atoms remaining after time t.
N_0 is the initial number of atoms.
λ is the decay constant, which is related to the half-life (T_1/2) by the equation:

$$ \lambda = \frac{\ln(2)}{T_{1/2}} $$

Example Calculation: Half-life of Iodine-125

The half-life of iodine-125 (¹²⁵I) is 60 days. Let's calculate the decay constant λ for this isotope.

$$ \lambda = \frac{\ln(2)}{60 \, \text{d}} = \frac{0.693}{60 \, \text{d}} \approx 0.01155 \, \text{d}^{-1} $$

This decay constant indicates how quickly iodine-125 undergoes electron capture decay. The higher the decay constant, the faster the decay process.

Example of Electron Capture in Medical Applications

While electron capture is not as commonly used in medical imaging as β⁺ decay, it has applications in certain types of radiotherapy and diagnostics. For example:

125I is used in medical treatments, such as in brachytherapy for cancer treatment, where a small radioactive source is placed inside or very close to a tumor.
The decay of 125I via electron capture results in gamma radiation that can be detected for imaging purposes.

Energy Released in Electron Capture

The energy released in electron capture decay is typically small compared to β⁺ decay because the proton-to-neutron transformation does not involve high-energy radiation. However, gamma rays and internal conversion can still occur in some cases, like in the transition of ¹²⁵Te from its excited state to the ground state.

The energy released during electron capture decay can be estimated using the Q value, which is the difference in binding energies between the parent and daughter nuclei, similar to β decay. However, this is often a small value compared to other types of decay.