Mark the correct options:

MCQ

A
An atom with a vacancy has smaller energy that a neutral atom.
B
K X-ray is emitted when a hole makes a jump from the K shell to some other shell.
C
The wavelength of K X-ray is smaller than the wavelength of L X-ray of the same material.
✓
B and C both

✓

Answer

Correct option: D.

B and C both

Explanation:
Energy of a vacant atom is higher than that of a neutral atom.
Hence, option (a) is incorrect.
K X-ray is emitted when an electron makes a jump to the K shell from some other shell. As a result, a positive charge hole is created in the outer shell. As the electron continuously moves to the K shell, the hole moves from the K shell to some other shell.
Hence, option (b) is correct.
K X-ray is emitted due to the transition of an electron from the L or M shell to the K shell and L X-ray is emitted due to the transition of an electron from the M or N shell to the L shell. The energy involved in the transition from the L or M shell to the K shell is higher than the energy involved in the transition from the M or N shell to the L shell. Since the energy is inversely proportional to the wavelength, the wavelength of the K X-ray is smaller than the wavelength of the L X-ray of the same material. Hence, option (c) is correct.
If $E_K$, $E_L$ and $E_M$ are the energies of K, L and M shells, respectively, then the wavelength of $\text{K}_\alpha$ X-ray $(\lambda_1)$ is given by
$\lambda_1=\frac{\text{hc}}{\text{E}_\text{K}-\text{E}_\text{L}}$
Here,
h = Planck's constant
c = Speed of light
Wavelength of the $\text{K}_\beta$ x-ray $(\lambda_2)$ is given by
$\lambda_2=\frac{\text{hc}}{\text{E}_\text{K}-\text{E}_\text{M}}$
As the difference of energies ($E_K - E_M$) is more than ($E_K- E_L$), $\lambda_2$ is less than$\lambda_1$.
Hence, option (d) is not correct.