First slide

Classical atomic models

Question

The potential energy of an electron in the second Bohr's orbit of the He⁺ion is x, Which cant be value x in this case ?

Moderate

A

-54.4 eV
B

-27.2 eV
C

-108.8 eV
D

-13.6 eV

Solution

Potential energy of the electron $= - \frac{4 π^{2} {mZ}^{2} e^{4} k^{2}}{n^{2} h^{2}}$
(PE) of H-atom in ground state (n = 1)
$= - \frac{4 π^{2} {me}^{4} k^{2}}{h^{2}} = 2 (- \frac{2 π^{2} {me}^{4} k^{2}}{h^{2}})$
$= 2 (- 13.6 eV) = - 27.2 eV$
Note : $E_{1} (H)$ in ground state $= \frac{2 π^{2} {me}^{4} k^{2}}{h^{2}} (\frac{Z^{2}}{n^{2}}) = - 27 .2 eV$
For He+ in second Bohr's orbit (n = 2, Z = 2)
$PE = - \frac{4 π^{2} {me}^{4} k^{2}}{h^{2}} (\frac{Z^{2}}{n^{2}}) = - 27 .2 eV$

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