The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is (ao is the Bohr rad

Question

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is (a_o is the Bohr radius)

a) $\frac{h^{2}}{4\pi^{2}ma_{o}^{2}}$ (b) $\frac{h^{2}}{16\pi^{2}ma_{o}^{2}}$ (c) $\frac{h^{2}}{32\pi^{2}ma_{o}^{2}}$ (d) $\frac{h^{2}}{64\pi^{2}ma_{o}^{2}}$

Accepted Answer

$K.E. = \frac{1}{2}mv^{2} = \frac{1}{2}m.\left( \frac{nh}{2\pi.mr} \right)^{2} = \frac{n^{2}h^{2}}{8\pi^{2}mr^{2}} = \frac{n^{2}h^{2}}{8\pi^{2}m.\left( a_{0}^{2}.n^{4} \right)} = \frac{h^{2}}{8\pi^{2}ma_{0}^{2}.n^{2}}$

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