✓ Board-verified
Physics · 2026 · 2 marks
CBSE 2026 · Region 1 · Set 2 · Q18
Find the ratio ((λ_a)/(λ_p)) of de Broglie wavelength λ_a associated with an alpha particle to de Broglie wavelength λ_p associated with a proton if…
Find the ratio $\displaystyle \left(\frac{\lambda_{\mathrm{a}}}{\lambda_{\mathrm{p}}}\right)$ of de Broglie wavelength $\displaystyle \lambda_{\mathrm{a}}$ associated with an alpha particle to de Broglie wavelength $\displaystyle \lambda_{\mathrm{p}}$ associated with a proton if both are moving with the (a) same velocity (b) same kinetic energy.
Marking-scheme solution
de-Broglie wavelength $\displaystyle \lambda=\dfrac{h}{mv}$
(a)
For same velocity $\displaystyle \lambda \alpha \dfrac{1}{m}$
$\displaystyle \dfrac{\lambda_{a}}{\lambda_{p}}=\dfrac{m_{p}}{m_{a}}$
$\displaystyle \because$ mass of alpha is four times of mass of proton. Hence $\displaystyle \dfrac{\lambda_{a}}{\lambda_{p}}=\dfrac{m_{p}}{4 m_{p}}$
$\displaystyle \dfrac{\lambda_{a}}{\lambda_{p}}=\dfrac{1}{4}$
(b)
For same kinetic energy $\displaystyle \lambda=\dfrac{h}{\sqrt{2 m K}}$
$\displaystyle \lambda \alpha \dfrac{1}{\sqrt{m}}$
$\displaystyle \dfrac{\lambda_{a}}{\lambda_{p}}=\dfrac{1}{2}$
All Dual Nature of Radiation and Matter questions2026 question paperNCERT solutions: Dual Nature of Radiation and MatterPractice Dual Nature of Radiation and Matter →
More from Dual Nature of Radiation and Matter
- The de-Broglie wavelength associated with an electron is 0.30 nm. Calculate: the speed, and the kinetic energy (in eV), of the electron.2022
- In a photoelectric experiment, the emitter plate is irradiated with radiation of 200 nm. The photocurrent becomes zero when the collector plate…2026
- Draw a plot of frequency v of incident radiations as a function of stopping potential V_0 for a given photo emissive material. What information can…2025
- A particle is associated with a de Broglie wave of wavelength 1.2 nm. The kinetic energy of the particle is made four times. Calculate the new value…2023
- de Broglie wavelength λ as a function of 1/(√ K), for two particles of masses m_1 and m_2 are shown in the figure. Here, K is the energy of the…2024
- The energy of a photon of wavelength 663 nm is2023
- Consider a neutron (mass m ) of kinetic energy E and a photon of the same energy. Let λ_n and λ_p be the de Broglie wavelength of neutron and the…2024
- Mention any three features of results of experiment on photoelectric effect which cannot be explained using the wave theory of light. In his…2025
CBSE Class 12 Physics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.