Q28 of 29 Page 73

A particle A with a mass mA is moving with a velocity v and hits a particle B (mass mB) at rest (one dimensional motion). Find the change in the de Broglie wavelength of the particle A. Treat the collision as elastic.

Mass of particle A = mA, Mass of particle B = mB

Initial velocity of A = v, initial velocity of B = 0


Initially, only particle A is moving.




After collision, let the velocity of the particle A be v1 and that of particle B be v2.


Then




Using conservation of momentum, Initial momentum will be same as final momentum.



Eq. 1 Since, this is an elastic collision, the Kinetic Energy shall also remain conserved.



Eq. 2




Dividing the above equation by Eq. 1, we get





Using these values in Eq. 2











Initial de-Broglie wavelength for particle A (i), with initial momentum as pi



Final de-Broglie wavelength for particle A , with final momentum as pf



Change in de-Broglie wavelength (∆λ)



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Consider an electron in front of metallic surface at a distance d (treated as an infinite plane surface). Assume the force of attraction by the plate is given as

Calculate work in taking the charge to an infinite distance from the plate. Taking d = 0.1nm, find the work done in electron volts. [Such a force law is not valid for d < 0.1nm].


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A student performs an experiment on photoelectric effect, using two materials A and B. A plot of Vstop vs v is given in Fig. 11.2.


(i) Which material A or B has a higher work function?


(ii) Given the electric charge of an electron = 1.6 × 10–19 C, find the value of h obtained from the experiment for both A and B. Comment on whether it is consistent with Einstein’s theory :


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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?]