First slide

Hydrogen -like ion

Question

Energy of the electron in $H e^{+}$ ion is four times the energy of the electron in the first excited state if hydrogen atom. Then orbital angular momentum of the electron in the above said $H e^{+}$ ion is

Moderate

A

$3 h / π$
B

$3 h / 2 π$
C

$2 h / π$
D

$h / π$

Solution

Suppose in $H e^{+}$ ion is in nth energy state and the hydrogen atom is in nth energy state.
$∴ - \frac{13.6 z^{2}}{n^{2}} = 4 \times (- 13.6 / 2^{2}) \Rightarrow n = \frac{2 \times 2}{\sqrt{4}} = 2$
$∴$ In the $H e^{+}$ ion, $L = n \frac{h}{2 π} = 2 \times \frac{h}{2 π} = \frac{h}{π}$

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