CBSE Class 12 Physics 2024: question 27

Hints

Open one hint at a time and try again before the next.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. Drawbacks of Rutherford's model: (1) An electron revolving round the nucleus is accelerated, so by classical electromagnetic theory it must radiate energy continuously. It would spiral into the nucleus, so the atom could not be stable. (2) As it spirals in, its frequency of revolution changes continuously, so the atom should emit a continuous spectrum. Atoms actually show line spectra.

   1 mark

2. Bohr's remedy: Bohr postulated that an electron revolves only in certain stable (stationary) orbits, for which its angular momentum $mvr=\frac{nh}{2\pi }$. In these orbits it does not radiate. Radiation is emitted only when the electron jumps from a higher orbit to a lower one, giving a photon of energy $h\nu =E_i-E_f$. This explains both the stability of the atom and the line spectrum.

   1 mark

3. In Bohr's model the radius of the nth orbit is $r_n=\frac{n^2{h}^2{\epsilon }_0}{\pi mZ{e}^2}$, so $r_n=k{n}^2$ and $r_1:r_2:r_3=1:4:9$. The spacing between successive orbits is $r_{n+1}-r_n=k[(n+1{)}^2-n^2]=k(2n+1)$. This depends on n (3k, 5k, 7k, …), so the orbits are not equally spaced.

   1 mark

Answer: Rutherford: atom unstable and spectrum should be continuous; Bohr: stationary non-radiating orbits with $L=nh/2\pi$ and quantised transitions; $r_n\propto n^2$ so spacing $k(2n+1)$ is not constant.

Revise the chapter

• Chapter: Atoms (notes, formulas, where marks are lost and every past question)
• Topic: Alpha-Particle Scattering and Rutherford's Model