Matter Waves: de Broglie Wavelength question from MHT CET 2026 (20 May, Shift 1)

Answer: (a)

1. Same $\lambda$ means same momentum $p = h/\lambda$.
2. Electron: $K = \dfrac{p^2}{2m} = \dfrac{h^2}{2m\lambda^2}$. Photon: $E = \dfrac{hc}{\lambda}$.
3. $\dfrac{K}{E} = \dfrac{h^2}{2m\lambda^2} \cdot \dfrac{\lambda}{hc} = \dfrac{h}{2\lambda mc}$
4. So the answer is (a).