Final Answer:
The atomic number and the mass number both stay the same. Thus the correct option is option (b).
Step-by-step explanation:
Gamma radiation, denoted by λ, does not alter the atomic number or the mass number of an atom. It is a type of electromagnetic radiation without mass or charge. Unlike alpha and beta decay, which involve changes in the atomic and mass numbers, gamma radiation is a high-energy photon emission from an excited nucleus.
In gamma decay, the nucleus transitions from a higher energy state to a lower one, releasing a gamma-ray photon. The emitted gamma ray carries energy but doesn't change the composition of the nucleus. Therefore, both the atomic number Z and mass number A remain constant.
To understand this conceptually, think of the nucleus as having excess energy in an excited state. The gamma decay allows the nucleus to release this excess energy without altering its fundamental structure. Mathematically, this can be represented as:
![\[ _(Z)^(A)X^* \rightarrow _(Z)^(A)X + \gamma \]](https://img.qammunity.org/2024/formulas/mathematics/high-school/afz0bkguw399khfkfvwi6dsimbofa70lbi.png)
Where X is the element, Z is the atomic number, and A is the mass number. The asterisk * indicates the excited state. Thus the correct option is option (b).