Question 325: Atoms & Nuclei

Question

As per given figure $A, B$ and $C$ are the first, second and third excited energy levels of hydrogen atom respectively. If the ratio of the two wavelengths $\left(\right.$ i.e. $\left.\frac{\lambda_{1}}{\lambda_{2}}\right)$ is $\frac{7}{4 n}$, then the value of $n$ will be __________.

Accepted Answer

$$
\begin{aligned}
& 	ext { As } \frac{1}{\lambda}=\mathrm{RZ}^2\left[\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}ight] \\
& \frac{1}{\lambda_1}=\mathrm{R}(1)^2\left[\frac{1}{(2)^2}-\frac{1}{(3)^2}ight]=\mathrm{R}\left(\frac{5}{36}ight)~~......(i) \\
& \& \frac{1}{\lambda_2}=\mathrm{R}(1)^2\left[\frac{1}{(3)^2}-\frac{1}{(4)^2}ight]=\mathrm{R}\left(\frac{7}{144}ight) ~~......(ii)
\end{aligned}
$$
(ii) $\div$ (i) gives
$$
\begin{aligned}
& \frac{\lambda_1}{\lambda_2}=\frac{7 / 144}{5 / 36}=\frac{7}{20}=\frac{7}{4 	imes 5} \\
& 	herefore \mathrm{n}=5
\end{aligned}
$$

Atoms & Nuclei

As per given figure A, B and C are the first, second and third excited energy levels of hydrogen atom respectively. If the ratio of the two wavelengths \left(\right. i.e. \left.\frac{\lambda_{1}}{\lambda_{2}}\right) is \frac{7}{4 n}, then the value of n will be __________.

Integer / Numeric Answer Type