The electron in a hydrogen atom makes a transition from M shell to L-shell. The ratio of magnitude of initial to final acceleration of the electron is

Options

A. `9:4`
B. `81:16`
C. `4:9`
D. `16:81`

Explanation

To solve the problem of finding the ratio of the magnitude of the initial to final acceleration of the electron in a hydrogen atom when it transitions from the M shell to the L shell, we can follow these steps:

### Step 1: Understand the Shells
In a hydrogen atom:
- The M shell corresponds to the principal quantum number \( n = 3 \).
- The L shell corresponds to the principal quantum number \( n = 2 \).

### Step 2: Formula for Acceleration
The centripetal acceleration \( a \) of an electron in a circular orbit can be expressed as:
\[ a \propto \frac{1}{n^4} \]
This means that acceleration is inversely proportional to the fourth power of the principal quantum number \( n \).

### Step 3: Calculate Initial and Final Acceleration
- For the M shell (initial state), where \( n = 3 \):
\[ a_M \propto \frac{1}{3^4} = \frac{1}{81} \]

- For the L shell (final state), where \( n = 2 \):
\[ a_L \propto \frac{1}{2^4} = \frac{1}{16} \]

### Step 4: Find the Ratio of Initial to Final Acceleration
Now, we can find the ratio of the initial acceleration \( a_M \) to the final acceleration \( a_L \):
\[ \text{Ratio} = \frac{a_M}{a_L} = \frac{\frac{1}{81}}{\frac{1}{16}} = \frac{16}{81} \]

### Conclusion
The ratio of the magnitude of the initial to final acceleration of the electron when it transitions from the M shell to the L shell is:
\[ \frac{16}{81} \]