Question

The energy level diagram of $K_{\alpha }$ x-ray emission is shown here. What is the correct inference?

• A. The arrow in the diagram represents the jump of an electron from the K shell to the L shell.
• B. The energy levels represent the energies of the atom when one electron is missing from respective shell.
• C. The energy of the atom in K shell is lesser than its energy in L shell, but the diagram shows K shell at higher energy; hence the diagram is incorrect.
• D. An x-ray carrying about 17 keV of energy will be radiated in the transition.

Answer 1

Answer: (B), (D)

An x-ray carrying about 17 keV of energy will be radiated in the transition.


The energy levels correspond to the energies of the atom when an electron is missing from the particular shells.
An electron in the K shell will be more tightly bound to the nucleus than one in the L shell, say. We will have to provide more energy to kick out a K-electron than an K-electron. In other words, the atom gains more energy when a K shell electron gets ejected compared to a higher shell electron.

When there is a vacancy in the K shell, the atom is at the K (n=1) energy level (higher). If an electron from the L (n=2) orbit jumps to K to fill the vacancy, the atom's energy falls to a level corresponding to a vacancy in the L shell. Remember that although the electron physically jumps from an outer shell to an inner shell, the atom's energy level falls, and the arrow in the diagram represents that drop in energy (which is opposite to the electron's transition, if we consider initial and final quantum numbers, but in the direction of the vacancy's transition).

In this process, the difference in energy is compensated by radiation of x-ray photons of energy equal to $\sim$ (20 keV- 3 keV) = $\sim$ 17 keV.