Q. 213.7( 3 Votes )
Assuming an electron is confined to a 1nm wide region, find the uncertainty in momentum using Heisenberg Uncertainty principle (Ref Eq 11.12 of NCERT Textbook). You can assume the uncertainty in position Δx as 1nm. Assuming p ≃ Δp, find the energy of the electron in electron volts.
According to the Heisenberg’s Uncertainty Principle
Here, h is the Plank’s constant, ∆x is the uncertainty in the position and ∆p is the uncertainty in the momentum of the electron. ∆x is given and is equal to 1nm = 10-9 m
As given in the question, we can treat ∆p as p in order to find the energy of the electron
Converting to eV by dividing by 1.6 x 10-19.
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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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