Photoelectric Effect

Q: Consider a 20 W bulb emitting light of wavelength 5000 Å and shining on a metal surface kept at a distance 2 m. Assume that the metal surface has work function of 2 eV and that each atom on the metal surface can be treatment as a circular disk of radius. 1.5 Å.

(i) Estimate number 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 ?

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

Q: Consider a thin target (10-2 m square, 10^-3 m thickness) of sodium, which produces a photocurrent of 100  μA when a light of intensity 100 W/m2 (λ = 660) falls on it. Find the probability that a photoelectron is produced when a photon strikes a sodium atom.
[Take density of Na = 0.97 kg/m³]

Q: A neutron beam of energy E scatters from atoms on a surface with a spacing d = 0.1 nm. The first maximum of intensity in the reflected beam occurs at θ= 30°. What is the kinetic energy E of the beam in eV ?

Q: Two particle A and B of de-Broglie wavelength 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)