(A)Calculate, in units of ?, the magnitude of the maximum orbital angular moment

Question

(A)Calculate, in units of ?, the magnitude of the maximum orbital angular momentum for an electron in a hydrogen atom for states with a principal quantum number of 9.00.

(B)Calculate, in units of ?, the magnitude of the maximum orbital angular momentum for an electron in a hydrogen atom for states with a principal quantum number of 41.0.

(C)Calculate, in units of ?, the magnitude of the maximum orbital angular momentum for an electron in a hydrogen atom for states with a principal quantum number of 206.

(D)Compare each with the value of n? postulated in the Bohr model. What trend do you see?

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            Where hbar = 1.0546*10-34 J.s

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=41,

L_max= sqrt(40 *41) hbar = 40.497* hbar

With n= 9,

L_max = sqrt(8* 9) hbar = 8.485* hbar

With n= 206,

L_max = sqrt(205 *206) hbar= 205.499* hbar

Note that for large n, sqrt( n ( n-1)) approximately equals n.

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.