Download App

Dual Nature of Radiation and Matter — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsDual Nature of Radiation and Matter2 Marks
Question
X-rays of wavelength $'\lambda'$ fall on a photosensitive surface, emitting electrons. Assuming that the work function of the surface can be neglected, prove that the de Broglie wavelength of electrons emitted will be $\sqrt{\frac{\text{h}\gamma}{2\text{mc}}}.$
✓

Answer

K.E. of electrons, Ek = energy of X-ray photon $=\frac{\text{hc}}{\lambda}$
$\therefore$ de Broglie wavelength, $\lambda_\text{B}=\frac{\text{h}}{\sqrt{2\text{mE}_\text{k}}}.$
But $\text{E}_\text{k}=\frac{\text{hc}}{\lambda}$
$\therefore\ \lambda_\text{B}=\frac{\text{h}}{\sqrt{2\text{m}\big(\frac{\text{hc}}{\lambda}\big)}}=\sqrt{\frac{\text{h}\lambda}{2\text{mc}}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Dual Nature of Radiation and Matter→Dual Nature of Radiation and Matter — all question types→Physics STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Distinguish between the terms 'average value' and 'rms value' of an alternating current. The instantaneous current from an a.c. source is I = 5 sin (314 t) ampere.
What are the average and rms values of the current?
→
When is a magnet said to be in stable equilibrium in a magnetic field?
→
At what rate should the earth rotate so that the apparent g at the equator becomes zero? What will be the length of the day in this situation?
→
An electric current of 5 A is flowing through a wire of area of cross-section $4 \times 10^{-6} m^2$. If the number density of charge carriers (free electrons) is $5 \times 10^{26}$ $m ^{-3}$. Find the drift velocity of the electrons.
→
A thin spherical shell of radius R lying on a rough horizontal surface is hit sharply and horizontally by a cue. Where should it be hit so that the shell does not slip on the surface?
→
Explain the process of thermonuclear fusion as a source of energy in the Sun.
→
You are riding in a car. The driver suddenly applies the brakes and you are pushed forward. Who pushed you forward?
→
The changes in a function y and the independent dy variable x are related as $\frac{\text{dy}}{\text{dx}}=\text{x}^2.$ Find y as a function of x.
→
Define equipotential surface.
→
Answer the following question:
The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations:
$\text{E}=\text{h v, p}=\frac{\text{h}}{\lambda}$
But while the value of λ is physically significant, the value of ν (and therefore, the value of the phase speed ν λ) has no physical significance. Why?
→