Question

Calculate the change in angular momentum of an electron when it jumps from the third orbit to the first orbit in a hydrogen atom.

Hint:

The angular momentum of an electron in orbit is quantized and depends on the principal quantum number \( n \).

Answer 1

The angular momentum \( L \) of an electron in a hydrogen atom is quantized and given by:
\[ L = n \hbar \] where \( n \) is the principal quantum number and \( \hbar \) is the reduced Planck's constant. For the third orbit, \( n = 3 \), and for the first orbit, \( n = 1 \). 
The change in angular momentum is:
\[ \Delta L = L_1 - L_3 = 1\hbar - 3\hbar = -2\hbar \] Since \( \hbar = 1.055 \times 10^{-34} \, {Js} \), the change in angular momentum is: \[ \Delta L = -2 \times 1.055 \times 10^{-34} = -2.11 \times 10^{-34} \, {Js}. \] Thus, the change in angular momentum is \( 2.11 \times 10^{-34} \, {Js} \).