Based on the presence of an emitted electron, the equation is most likely modeling beta-minus decay (a).
The equation you provided doesn't directly tell us which type of radioactive decay it models. However, we can analyze the equation to make some educated guesses:
The equation: X -> Y + e-
Components:
X: Represents the decaying nucleus.
Y: Represents the daughter nucleus after the decay.
e-: Represents an electron emitted during the decay.
Based on the presence of an emitted electron, we can eliminate options (c) and (d):
Beta-plus decay (c) involves the emission of a positron (e+) instead of an electron (e-).
Alpha decay (d) involves the emission of an alpha particle (α), which consists of two protons and two neutrons.
Now, we're left with options (a) and (b):
Beta-minus decay (a) involves the conversion of a neutron in the nucleus into a proton, along with the emission of an electron and an antineutrino. This process would be represented by the equation: n -> p + e- + ν.
Gamma decay (b) involves the emission of a gamma ray from an excited nucleus to a lower energy state. This process doesn't involve any change in the number of protons or neutrons, so it wouldn't be represented by the equation X -> Y + e-.