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Energy difference between the successive levels in same shell of atom

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Hydrogen-like atom is in an external magnetic field $B=1.6 \ T$.
a) What is the energy difference ($\triangle E$) between the successive $m_l$-levels in same $l$-shell of atom? (Give the answer in $eV$.)

I tried this:

$E_n = -\frac{13.6 \ eV}{n^2}$

$\triangle E = E_2 - E_1 = -\frac{13.6 \ eV}{2^2} - (-\frac{13.6 \ eV}{1^2}) = -\frac{13.6 \ eV}{4} + 13.6 \ eV =10.2 \ eV$

But I didn't get correct answer. So please help me, how should I get correct answer? Any help is appreciated, thanks in advance!

asked Mar 18, 2017 in Physics Problems by RedRose (140 points)

1 Answer

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Best answer

The question says the $m_l$ levels are in the same $l$ shell. This means that $n$ and$l$ are the same. You are using the wrong formula. You need a formula which involves magnetic field.

The splitting of the energies of the $m_l$ levels is called the Zeeman Effect. The splitting is $\Delta E=\mu B$ where $\mu$ is the Bohr magneton.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/zeeman.html#c3

answered Mar 18, 2017 by sammy gerbil (28,876 points)
selected Mar 18, 2017 by RedRose
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