In X-rays spectrum, transition of an electron from an outer shell to an inner shell gives a characteristics X-rays spectral line. If we consider the spectrum line `K_(beta),L_(beta)n and M_(alpha)` , them

Options

A. `K_(beta) and L_(beta)` have a common inner shell
B. `K_(beta) and L_(beta)` have a common outer shell
C. `L_(beta) and M_(alpha)` have a common outer shell
D. `L_(beta) and M_(alpha)` have a common inner shell

Explanation

To solve the problem regarding the transitions in the X-ray spectrum and the characteristics of K-beta, L-beta, and M-alpha spectral lines, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Energy Levels**:
- We have different energy levels represented by K, L, M, and N shells. The K shell is the innermost shell, followed by L, M, and N shells.

2. **Identifying the Transitions**:
- **K-beta (Kβ)**: This transition involves an electron moving from the M shell to the K shell. This means the outer shell is M and the inner shell is K.
- **L-beta (Lβ)**: This transition involves an electron moving from the N shell to the L shell. Here, the outer shell is N and the inner shell is L.
- **M-alpha (Mα)**: This transition involves an electron moving from the N shell to the M shell. For this transition, the outer shell is N and the inner shell is M.

3. **Analyzing Common Shells**:
- For **K-beta**: Outer shell = M, Inner shell = K.
- For **L-beta**: Outer shell = N, Inner shell = L.
- For **M-alpha**: Outer shell = N, Inner shell = M.
- Now, we need to check for common outer and inner shells among these transitions.

4. **Finding Common Outer Shells**:
- K-beta and L-beta: Common outer shell = None (M and N are different).
- K-beta and M-alpha: Common outer shell = None (M and N are different).
- L-beta and M-alpha: Common outer shell = N (both have N as the outer shell).

5. **Finding Common Inner Shells**:
- K-beta and L-beta: Common inner shell = None (K and L are different).
- K-beta and M-alpha: Common inner shell = None (K and M are different).
- L-beta and M-alpha: Common inner shell = None (L and M are different).

6. **Conclusion**:
- The only commonality found is that L-beta and M-alpha share a common outer shell, which is the N shell.

### Final Answer:
The correct option is that L-beta and M-alpha have a common outer shell, which is option C.