Solveeit Logo
Login

Question

Question: The \( {K_\alpha } \) X-ray of molybdenum has wavelength \( 71pm \) . If the energy of a molybdenum ...

The Kα{K_\alpha } X-ray of molybdenum has wavelength 71pm71pm . If the energy of a molybdenum atom with KK electron knocked out is 23.32 keV23.32{\text{ keV}} , what will be the energy of this atom when an L electron is knocked out?

Explanation

Solution

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,NK,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=hcλE = \dfrac{{hc}}{\lambda }
Where E is the energy, C is the speed of light , h is planck's constant and λ\lambda is the wavelength of light.
E=4.4×10−15×3×10871×10−8 ⇒E=17.5 keV 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.
EK−EL=17.5 keV ⇒EL=EK−17.5 keV ⇒EL=23.32−17.5 ⇒EL=5.82 keV  {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).