### Calculate the cutoff wavelength and the threshold frequency

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Question 1: Molybdenum has a work function of 4.2 eV.

(a) Find the cutoff wavelength and the threshold frequency for the photoelectric effect.

(b) Calculate the stopping potential if the incident light has a wavelength of 180 nm.

Question 2: A photon of initial energy 0.1 MeV undergoes Comptom scattering at an angle 0f 60o. Remember these electrons have relativistic velocities. Find

(a) the energy of the scattered photon

(b) the recoil energy of the electron

(c) the scattering angle of the electron.

Question 3:  A 0.0016 nm photon scatters from a free electron, for what (photon) scattering angle will the recoiling electron and scattered photon have the same kinetic energy?

Question 4: A neutron beam with a speed of 0.6 m/s is directed through a double slit with 0.75mm separation. An array of detectors is placed 12m from the slits.

(a) What is the de Broglie wavelength of the neutrons?

(b) How far off axis is the first zero intensity point on the detector array?

Question 5: An electron has a wave function

ψ(x) = √2/L sin (2πx/L )

Find the probability of finding the electron between x=0 and x=L/4.

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