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Physics · 2023 · 3 marks
CBSE 2023 · Region 5 · Set 2 · Q30
(a) (i) Write the limitations of Rutherford's model of atom. (ii) The wavelength of the second line of the Balmer series in the hydrogen spectrum is…
(i)
Write the limitations of Rutherford's model of atom.
(ii)
The wavelength of the second line of the Balmer series in the hydrogen spectrum is $\displaystyle 4861 \AA$. Calculate the wavelength of the first line of the same series.
(i)
Increase in the intensity of the radiation causing photo-electric emission from a surface, does not affect the maximum K.E. of the photo electrons. Explain.
(ii)
The photon emitted during the de-excitation from the first excited level to the ground state of hydrogen atom is used to irradiate a photo cathode in which stopping potential is $\displaystyle 5$ V . Calculate the work function of the cathode used.
Marking-scheme solution
(i)
1. Rutherford Model was unable to explain the stability of atom.
2. It could not explain the existence of the line spectrum.
(ii)
\(\displaystyle \frac{1}{\lambda}=\mathrm{R}\left[\frac{1}{n_{\mathrm{i}}^{2}}-\frac{1}{n_{f}^{2}}\right]\)
\[\frac{1}{\lambda_{2}}=\mathrm{R}\left[\frac{1}{2^{2}}-\frac{1}{4^{2}}\right]
\]
\[\frac{1}{\lambda_{2}}=\frac{3 \mathrm{R}}{16}-\cdots \cdots-(\mathrm{i})
\]
\[\frac{1}{\lambda_{1}}=\mathrm{R}\left[\frac{1}{2^{2}}-\frac{1}{3^{2}}\right]
\]
\[\frac{1}{\lambda_{1}}=\frac{5 \mathrm{R}}{36}
\]
\[\frac{\lambda_{1}}{\lambda_{2}}=\frac{36}{5 \mathrm{R}} \frac{3 \mathrm{R}}{16}
\]
\[\lambda_{1}=\frac{36 \times 3}{5 \times 16} \times 4861
\]
\[\lambda_{1}=6562.35 \AA
\]
(i)
\[h v=\phi_{o}+K_{\max }
\]
It is evident from the above equation that the maximum kinetic energy depends on the frequency of incident radiation and is independent of the intensity of the radiations.
(ii)
Energy carried by the photon
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CBSE Class 12 Physics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.