Q. 234.5( 2 Votes )
Two particles A and B of de Broglie wavelengths λ1 and λ2 combine to form a particle C. The process conserves momentum. Find the de Broglie wavelength of the particle C. (The motion is one dimensional).
(Since the motion is one-dimensional, we will take into account only the magnitude of the momentum). Momentum of particle A (pA) with wavelength will be given as
Momentum of particle B (pB ) with wavelength will be given as
The momentum of the system before collision =
The momentum of the system after collision = where is the momentum of particle C.
Let 3 be the de-Broglie wavelength of particle C, then
Using conservation of momentum
This result is true considering both particles are moving in one direction. If they are moving in opposite direction, we can take one direction as positive and the other as negative and repeat the above steps.
If they are moving in opposite directions then
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Consider a 20 W bulb emitting light of wavelength and shining on a metal surface kept at a distance 2m. Assume that the metal surface has work function of 2 eV and that each atom on the metal surface can be treated as a circular disk of radius .
(i) Estimate no. of photons emitted by the bulb per second. [Assume no other losses]
(ii) Will there be photoelectric emission?
(iii) How much time would be required by the atomic disk to receive energy equal to work function (2 eV)?
(iv) How many photons would atomic disk receive within time duration calculated in (iii) above?
(v) Can you explain how photoelectric effect was observed instantaneously?
[Hint: Time calculated in part (iii) is from classical consideration and you may further take the target of surface area say 1cm2 and estimate what would happen?]
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