Question

The $ {K_\alpha } $ X-ray of molybdenum has wavelength $ 71pm $ . If the energy of a molybdenum atom with $ K $ electron knocked out is $ 23.32{\text{ keV}} $ , what will be the energy of this atom when an L electron is knocked out?

Answer 1

Hint: We know that wavelength is the distance between two corresponding waves. The electronic configuration is used to describe how the electrons are distributed in atomic orbitals. The electrons accommodated in a shell are denoted by principal quantum number and there are four shells represented as $ K,L,M,N $ and the subshells are denoted by azimuthal quantum number. The energy of an orbital is represented by a sum of principal and azimuthal quantum number.

Complete step by step solution
The formula for finding the energy is ,
 $ E = \dfrac{{hc}}{\lambda } $
Where E is the energy, C is the speed of light , h is planck's constant and $ \lambda $ is the wavelength of light.
$ E = \dfrac{{4.4 \times {{10}^{ - 15}} \times 3 \times {{10}^8}}}{{71 \times {{10}^{ - 8}}}} \\
 \Rightarrow E = 17.5{\text{ keV}} \\
 $
We need to find the energy when the L electron is knocked out so that the energy difference between K&L equals the net energy emitted.
 $
  {E_K} - {E_L} = 17.5{\text{ keV}} \\
   \Rightarrow {E_L} = {E_K} - 17.5{\text{ keV}} \\
   \Rightarrow {E_L} = 23.32 - 17.5 \\
   \Rightarrow {E_L} = 5.82{\text{ keV}} \\
 $

Additional Information
Electron Configurations are useful for:
-Determining the valency of an element.
-Predicting the properties of a group of elements (elements with similar electron configurations tend to exhibit similar properties).
-Interpreting atomic spectra.
-The Aufbau principle dictates that electrons will occupy the orbitals having lower energies before occupying higher energy orbitals.

Note

Pauli exclusion principle: It states that a maximum of two electrons, each having opposite spins, can slot in an orbital. Therefore, if the principal, azimuthal, and magnetic numbers are the same for 2 electrons, they have to have opposite spins.
Hund’s Rule: This rule describes the order within which electrons are filled altogether the orbitals belonging to a subshell.
In order to maximise the overall spin, the electrons within the orbitals that only contain one electron all have the identical spin (or the identical values of the spin quantum number).