Question #86678
The energy of the lowest allowed level for an electron in a 1-D box is 10.0 eV. Can the electron ever have an energy of 200 eV? Justify.
1
Expert's answer
2019-03-20T11:46:09-0400

The allowed energies for an electron in a 1-D box

En=n2π222mL2,n=1,2,3,...E_n=\frac{n^2\pi^2\hbar^2}{2mL^2}, \quad n=1,2,3,...

So

EnEk=n2k2\frac{E_n}{E_k}=\frac{n^2}{k^2}

200eV10.0eV=n212\frac{200\:\rm{eV}}{10.0\:\rm{eV}}=\frac{n^2}{1^2}

n=20.0=4.47n=\sqrt{20.0}=4.47

Since n is non-integer, so the electron would not have an energy of 200 eV.


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Comments

AINEBYOONA chriscent
25.09.21, 01:00

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