Question

-Calculate the magnitude of the maximum orbital angular momentum Lmax for an electron in a hydrogen atom for states with a principal quantum number of 8.

Express your answer in units of ℏ to three significant figures.

-Calculate the magnitude of the maximum orbital angular momentum Lmax for an electron in a hydrogen atom for states with a principal quantum number of 48.

Express your answer in units of ℏ to three significant figures.

-Calculate the magnitude of the maximum orbital angular momentum Lmax for an electron in a hydrogen atom for states with a principal quantum number of 247.

Express your answer in units of ℏ to three significant figures.

Answer 1

The magnitude of the orbital angular momentum of the electron depends on the orbital quantum number l as

L = sqrt( l(l+1) ) hbar

For given principal quantum number n, the maximum value of l is n-1.( l= 0, 1, 2, ..., n-1).

So for given n, the maximum magnitude of orbital angular momentum is

L_max = sqrt(( n-1)n ) hbar

With n=48, L_max= sqrt(48 x47) h_bar = 47.5h_bar
With n= 8, L_max = sqrt(8x7) h_bar = 7.48h_bar
With n= 247, L_max = sqrt(247x246) h_bar= 246.5h_bar