First slide

Bohr Model of the Hydrogen atom.

Question

The frequency of the first line of Balmer series in hydrogen atom is $v_{0}$ Hz. The frequency v of the line emitted by a single ionized helium atom is

Moderate

A

$(2 v_{0}) H z$
B

$(4 v_{0}) Hz$
C

$(v_{0} / 2) Hz$
D

$(v_{0} / 4) Hz$

Solution

$v = Z^{2} R c [\frac{1}{{n_{1}}^{2}} - \frac{1}{{n_{2}}^{2}}] v_{0} = R c [\frac{1}{2^{2}} - \frac{1}{3^{2}}] = R c (\frac{9 - 4}{36}) or v_{0} = \frac{5 R c}{36} Further v = (2)^{2} R c [\frac{1}{2^{2}} - \frac{1}{3^{2}}] = \frac{20 R c}{36} \frac{v}{v_{0}} = 4 or v = 4 v_{0}$

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