Radioactive `._27^60Co` is transformed into stable `._28^60`Ni by emitting two `gamma`-rays of energies

Options

A. 1.33 MeV and 1.17 MeV in succession
B. 1.17 MeV and 1.33 MeV in succession
C. 1.37 MeV and 1.13 MeV in succession
D. 1.13 MeV and 1.37 MeV in succession

Explanation

To solve the problem of how radioactive \( _{27}^{60}Co \) (Cobalt-60) transforms into stable \( _{28}^{60}Ni \) (Nickel-60) by emitting two gamma rays, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Decay Process**:
- Cobalt-60 undergoes beta decay to transform into Nickel-60. In beta decay, a neutron in the cobalt nucleus is converted into a proton, resulting in the emission of a beta particle (electron) and an antineutrino. This increases the atomic number from 27 (Cobalt) to 28 (Nickel) while keeping the mass number the same (60).

2. **Identify the Energy Emissions**:
- After the beta decay, the newly formed Nickel-60 nucleus is in an excited state. To reach a stable state, it emits two gamma rays. The energies of these gamma rays are given as 1.17 MeV and 1.33 MeV.

3. **Write the Decay Equation**:
- The overall transformation can be represented as:
\[ _{27}^{60}Co \rightarrow _{28}^{60}Ni + \beta^- + \bar{\nu} + \gamma (1.17 \, \text{MeV}) + \gamma (1.33 \, \text{MeV}) \]
- Here, \( \beta^- \) represents the emitted beta particle, and \( \bar{\nu} \) is the antineutrino.

4. **Illustrate the Energy Levels**:
- You can visualize the process with an energy level diagram:
- Start with the Cobalt-60 nucleus at a higher energy level.
- After beta decay, it drops to an excited state of Nickel-60.
- The first gamma emission (1.33 MeV) brings it to a lower excited state.
- The second gamma emission (1.17 MeV) brings it down to the ground state of Nickel-60.

5. **Final State**:
- The final state is the stable Nickel-60 nucleus, which has released energy in the form of two gamma rays.

### Summary of the Process:
- Cobalt-60 undergoes beta decay to become Nickel-60.
- Nickel-60 emits two gamma rays (1.17 MeV and 1.33 MeV) to reach its stable state.