Question 382: Atoms & Nuclei

Question

For hydrogen atom, $$\lambda_{1}$$ and $$\lambda_{2}$$ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of $$\lambda_{1}$$ and $$\lambda_{2}$$ is $$\frac{x}{32}$$. The value of $$x$$ is __________.

Accepted Answer

$\frac{1}{\lambda}=\mathrm{RZ}^{2}\left[\frac{1}{\mathrm{n}_{1}^{2}}-\frac{1}{\mathrm{n}_{2}^{2}}ight]$
$$
\begin{aligned}
& \frac{1}{\lambda_{1}}=\mathrm{RZ}^{2}\left[\frac{1}{1^{2}}-\frac{1}{3^{2}}ight]=\frac{8}{9} \mathrm{RZ}^{2} 
 ........(1)\\ 
& \frac{1}{\lambda_{2}}=\mathrm{RZ}^{2}\left[\frac{1}{1^{2}}-\frac{1}{2^{2}}ight]=\frac{3}{4} \mathrm{RZ}^{2} ........(2)
\end{aligned}
$$
$$
\begin{gathered}
1 / 2 \Rightarrow \frac{\lambda_{2}}{\lambda_{1}}=\frac{8}{9} 	imes \frac{4}{3}=\frac{32}{27} \\
\frac{\lambda_{1}}{\lambda_{2}}=\frac{27}{32}
\end{gathered}
$$

Atoms & Nuclei

For hydrogen atom, $\lambda_{1} and \lambda_{2} are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of \lambda_{1} and \lambda_{2} is \frac{x}{32}. The value of x$ is __________.

Choose the correct answer: