Question 459: 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

Using Rydberg's formula
$$\frac{1}{\lambda_1}=\mathrm{R}\left[\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}ight]=\mathrm{R}\left[\frac{1}{1^2}-\frac{1}{3^2}ight]=\frac{8}{9} \mathrm{R}$$
Similarly, $\frac{1}{\lambda_2}=R\left[\frac{1}{1^2}-\frac{1}{2^2}ight]=\frac{3}{4} R$
$$\begin{array}{ll}
	herefore & \frac{\frac{1}{\lambda_1}}{\frac{1}{\lambda_2}}=\frac{\frac{8}{9} \mathrm{R}}{\frac{3}{4} R} \
	herefore \quad & \frac{\lambda_1}{\lambda_2}=\frac{27}{32} \
	herefore \quad & x=27
\end{array}$$

Answer

3

Answer

9

Answer

27

Answer

81

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

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