Can L- X-ray of one material have shorter wavelength than K- X-ray of another-

An L alpha; X ray is emitted when an electron jumps from the M to the L shell, and a K alpha; X ray is emitted when an electron jumps from the L to the K sh ...

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Byju's Answer

Standard XII

Physics

Intensity in Photon Model

Can Lα X-ray ...

Question

Can Lα X-ray of one material have shorter wavelength than Kα X-ray of another?

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Solution

An L_α X-ray is emitted when an electron jumps from the M to the L shell, and a K_α X-ray is emitted when an electron jumps from the L to the K shell. Less energy is involved when an electron jumps from the M to the L shell than when it jumps from the L to the K shell. Also, wavelength of a photon is inversely related to its energy. Therefore, an L_α X-ray has higher wavelength than a K_α X-ray for the same material.

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Q. 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 K_α X-ray is smaller than the wavelength of K_β X-ray of the same material.

The wavelengths of $K_{α}$ and $L_{α}$ X-rays of a material are 21.3 pm and 141 pm respectively. Find the wavelength of $K_{β}$ X-ray of the material.