To solve the problem, we need to find the ratio of the time periods of revolution \( T_{1,2} \) and \( T_{2,1} \) in Bohr's model for unielectronic atoms.
### Step-by-step Solution:
1. **Understand the Formula**:
In Bohr's model for unielectronic atoms, the time period of revolution \( T_{n,z} \) is proportional to \( \frac{n^3}{Z^2} \), where \( n \) is the principal quantum number (shell number) and \( Z \) is the atomic number.
2. **Calculate \( T_{1,2} \)**:
- For \( T_{1,2} \):
- Here, \( n = 1 \) and \( Z = 2 \).
- Thus, \( T_{1,2} \propto \frac{1^3}{2^2} = \frac{1}{4} \).
3. **Calculate \( T_{2,1} \)**:
- For \( T_{2,1} \):
- Here, \( n = 2 \) and \( Z = 1 \).
- Thus, \( T_{2,1} \propto \frac{2^3}{1^2} = \frac{8}{1} = 8 \).
4. **Find the Ratio \( \frac{T_{1,2}}{T_{2,1}} \)**:
- Now, we need to find the ratio \( \frac{T_{1,2}}{T_{2,1}} \):
\[
\frac{T_{1,2}}{T_{2,1}} = \frac{\frac{1}{4}}{8} = \frac{1}{4} \times \frac{1}{8} = \frac{1}{32}
\]
5. **Express the Ratio**:
- Therefore, the ratio \( T_{1,2} : T_{2,1} = 1 : 32 \).
### Final Answer:
The value of \( T_{1,2} : T_{2,1} \) is \( 1 : 32 \).
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