Q. In which of the following transitions will the wavelength be minimum?

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A

$n = 6$ to $n = 4$

B

$n = 4$ to $n = 2$

C

$n = 3$ to $n = 1$

D

$n = 2$ $t o$ $n = 1$

Solution:

The wavelength $\frac{1}{λ} = R (\frac{1}{( n _{f} ) ^{2}} - \frac{1}{( n _{i} ) ^{2}})$ , $λ$ is the minimum for which $(\frac{1}{( n _{f} ) ^{2}} - \frac{1}{( n _{i} ) ^{2}}) = C$ is the maximum. We need to check wavelength for each possible transition and the compare it.
Among all the transitions given, the transition when $n_{f} = 1$ and $n_{i} = 3$ , $C$ is maximum.
Therefore, $λ$ is minimum when $n_{f} = 1$ and $n_{i} = 3$ .