a.) Calculate the magnitude of the maximum orbital angular momentum L max for an

Question

a.) 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 ? to three significant figures.

b.)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 33.

Express your answer in units of ? to three significant figures

c.)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 204.

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

Explanation / Answer

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=33, L_max= sqrt(32 *33) hbar =32.5 hbar
With n= 8, L_max = sqrt(7*8) hbar = 7.5 hbar
With n= 204, L_max = sqrt(204*203) hbar= 203.5 hbar

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