Question

Mark the correct options.
(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.
(d) The wavelength of Kα X-ray is smaller than the wavelength of Kβ X-ray of the same material.

Answer 1

The correct answers are (b) and (c).

EXPLANATION:

• (b) When the hole jumps to some other shell from the K shell, K X-ray is emitted.  

• (c) K X-ray’s wavelength is smaller than the L x-ray’s wavelength belonging to the same material.

• A vacant atom’s energy is more than the neutral atom. So, option (a) is not correct.

• When there is a jump of electron from some other shell to the K shell, K X-ray is emitted. In the outer shell, a positive charge hole is formed as a result of this.

• There will be a movement to some other shell from the K shell when there is a continuous movement of electron to the K shell. So, option (b) is correct.

• Due to the electron transition, the emission of K X-ray takes place. This happens when there is an electron transaction to the K shell from M or L shell. The involved energy in the transition to the K shell from the M or L shell is greater than the involved energy in the transition to the L shell from the N or M shell.

• Subsequently, to the wavelength, the energy is inversely proportional, and the K x-ray’s wavelength is smaller than the L X-ray’s wavelength of the same material. So, the option (c) is correct.

• If EL, EK, and EM are the energies of L, K, and M shells, correspondingly, then the Kα X-ray’s wavelength λ1 is shown as λ1 = hcEK - EL

• where,
• h = Constant of Planck

• c = light’s speed  

• Kβ X-ray’s wavelength λ2 is shown as

• λ2 = hcEK - EM

• Energy difference (EK – EL) is less than (EK – EM), λ1 is greater than λ2. So, the option (d) is wrong.