✓ Board-verified
Physics · 2024 · 3 marks
CBSE 2024 · Region 2 · Set 2 · Q26
(a) Briefly explain de Broglie hypothesis for wave nature of matter. (b) Find the ratio of de Broglie wavelength associated with a proton and an…
(a)
Briefly explain de Broglie hypothesis for wave nature of matter.
(b)
Find the ratio of de Broglie wavelength associated with a proton and an alpha particle when both are
(i)
accelerated from rest through the same potential difference, and
(ii)
moving with the same kinetic energy.
Marking-scheme solution
(a)
Moving particles of matter display wave-like properties under suitable conditions.
The wavelength $\displaystyle \lambda$ associated with a particle of momentum p is given as:
$\displaystyle \lambda=\frac{h}{p}=\frac{h}{m v}$
$\displaystyle \lambda$ is the attribute of a wave while momentum is a typical attribute of a particle.
(b)(i)
$\displaystyle \lambda=\frac{h}{\sqrt{2 m e V}}$
$\displaystyle \frac{\lambda_{p}}{\lambda_{\alpha}}=\sqrt{\frac{2 \times 4 m_{p} \times 2 e \times V}{2 \times m_{p} \times e \times V}}$
$\displaystyle =2 \sqrt{2}$
(ii)
$\displaystyle \lambda=\frac{h}{\sqrt{2 m K}}$
$\displaystyle \frac{\lambda_{p}}{\lambda_{\alpha}}=\sqrt{\frac{2 \times 4 m_{p} \times K}{2 \times m_{p} \times K}}$
$\displaystyle =2$
All Dual Nature of Radiation and Matter questions2024 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 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.