First slide

Bohr's atom model

Question

If wavelength of photon emitted due to transition of an electron from the third orbit to the first orbit in a hydrogen atom is $λ$ then the wavelength of photon emitted due to transition of electron from the fourth orbit to the second orbit will be

Moderate

A

$\frac{128}{27} λ$
B

$\frac{25}{9} λ$
C

$\frac{36}{7} λ$
D

$\frac{125}{11} λ$

Solution

$\begin{array}{rcl} \frac{1}{λ} & = & R [\frac{1}{1^{2}} - \frac{1}{3^{2}}] \Rightarrow λ = \frac{9}{8 R} \\ Again, \frac{1}{λ^{'}} & = & R [\frac{1}{2^{2}} - \frac{1}{4^{2}}] \Rightarrow λ^{'} = \frac{16}{3 R} \\ Now, \frac{λ^{'}}{λ} & = & \frac{16}{3 R} \times \frac{8 R}{9} or λ^{'} = \frac{128}{27} λ \end{array}$

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