Given below are two statements:\ Statement I: The Paschen spectral line for a Hydrogen atom with th

Question

Given below are two statements:\ Statement I: The Paschen spectral line for a Hydrogen atom with the highest energy is located at $\frac{1}{9}R_{\mathrm{H}} \mathrm{cm}^{-1}$ (where $R_{\mathrm{H}}$ is the Rydberg constant).\ Statement II: When the temperature of a black body increases, the maximum intensity of emission shifts to a higher frequency.\ In the light of the above statements, choose the correct answer from the options given below.

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(c) : The highest energy line (shortest wavelength) in the Paschen series corresponds to the transition from $n_2=\infty$ to $n_1=3$. The wave number is $\bar{
u} = R_{\mathrm{H}}\left(\frac{1}{3^2} - \frac{1}{\infty^2}ight) = \frac{1}{9}R_{\mathrm{H}} \mathrm{cm}^{-1}$. Hence, Statement I is true. According to Wien's displacement law, $\lambda_{\mathrm{max}} \propto \frac{1}{T}$. As temperature $T$ increases, $\lambda_{\mathrm{max}}$ decreases, which means the corresponding frequency ($
u_{\mathrm{max}} = \frac{c}{\lambda_{\mathrm{max}}}$) increases. Hence, Statement II is also true.