Question

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

• A. $n=6$ to $n=4$
• B. $n=4$ to $n=2$
• C. $n=3$ to $n=1$
• D. $n=2$ $to$ $n=1$

Answer 1

Answer: (C)

The wavelength $\frac{1}{\lambda }=R\left(\frac{1}{\left(n_{f}\right)^{2}} - \frac{1}{\left(n_{i}\right)^{2}}\right)$ , $\lambda $ is the minimum for which $\left(\frac{1}{\left(n_{f}\right)^{2}} - \frac{1}{\left(n_{i}\right)^{2}}\right)=C$ 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, $\lambda $ is minimum when $n_{f}=1$ and $n_{i}=3$ .