Question: Q. 4. (i) Write two important limitations of Rutherford model which could not explain the observed features of atomic spectra. How were these explained in Bohr’s model of hydrogen atom? Use the Rydberg formula to calculate the wavelength of the $\mathrm{H}_{\alpha}$ line. (Take $\mathrm{R}=\mathbf{1 . 1 \times 1 0 ^ { 7 }} \mathrm{m}^{-1}$ ).
(ii) Using Bohr’s postulates, obtain the expression for the radius of the $n^{\text {th }}$ orbit in hydrogen atom.
R U [Delhi I, II, III 2015]
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Solution:
Ans. (i) (a) Electron moving in a circular orbit around the nucleus would get accelerated, therefore it would spiral into the nucleus, as it looses its energy.
(b) It must emit a continuous spectrum. $\mathbf{1}$ According to Bohr’s model of hydrogen atom,
(a) Electron in an atom can revolve in certain stable orbits without the emission of radiant energy. $1 / 2$
(b) Energy is released/absorbed only, when an electron jumps from one stable orbit to another stable orbit. This results in a discrete spectrum $\quad \mathbf{1}$
$$ \begin{align*} & \frac{1}{\lambda}=\mathrm{R}\left(\frac{1}{2^{2}}-\frac{1}{3^{2}}\right) \ & \frac{1}{\lambda}=1.1 \times 10^{7}\left(\frac{1}{4}-\frac{1}{9}\right) \ & \lambda=656.3 \mathrm{~nm} \tag{1} \end{align*} $$
(ii) Try yourself Similar to Q. 3 (i) LAQ.
