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Modern Physics
Found in: Page 344
Modern Physics

Modern Physics

Book edition 2nd Edition
Author(s) Randy Harris
Pages 633 pages
ISBN 9780805303087

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Short Answer

A hydrogen atom is subjected to a magnetic field B strong enough to completely overwhelm the spin-orbit coupling. Into how many levels would the 2p level split, and what would be the spacing between them?

5 levels,

And energy difference is E=ehB2m

See the step by step solution

Step by Step Solution

Step 1: total energy of magnetic field

In the case of a strong magnetic field B such as this one, the total energy E is given by

E=ehB2m(ml+ms)+Eo...................(1)

where Eo is the zero-field energy data-custom-editor="chemistry" (B=0).

Step 2: find level splits

The possible values for ml are l=1

ml=-1,0,1.............2

Since ms can have values of ±12, we conclude that the 2p level splits into 3+2=5 levels, since there are 3 possible values for ml and 2 possible values for ms.

The quantity ml+2ms can have values of

role="math" localid="1658468430759" ml+2ms=-2,-1,0,1,2............3

For example, let us take the following two levels:ml+2ms=1 and ml+2ms=2.

Step 3: energy difference ∆E

The energy difference E is then (we use Eq. (l))

E=ehB2m2-1E=ehB2m

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