CBSE Class 12 Physics sample paper 2023-24: question 18

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. de Broglie wavelength of the electron: $\lambda =\frac{h}{mv}$, so $v=\frac{h}{m\lambda }$ ...(i)

   ½ mark

2. Energy of a photon of wavelength $\lambda$: $E=\frac{hc}{\lambda }$ ...(ii)

   ½ mark

3. Kinetic energy of the electron: $K=\frac{1}{2}m{v}^2=\frac{1}{2}m\frac{h^2}{m^2{\lambda }^2}=\frac{h^2}{2m{\lambda }^2}$ ...(iii)

   ½ mark

4. Dividing (ii) by (iii): $\frac{E}{K}=\frac{hc}{\lambda }\cdot \frac{2m{\lambda }^2}{h^2}=\frac{2\lambda mc}{h}$. Hence $E=\frac{2\lambda mc}{h}K$.

   ½ mark

Answer: $E/K=2\lambda mc/h$ (shown).

Revise the chapter

• Chapter: Dual Nature of Radiation and Matter (notes, formulas, where marks are lost and every past question)
• Topic: de Broglie Wavelength