Photoelectric Effect

Q: (i) In the explanation of photoelectric effect, we assume one photon of frequency ν collides with an electron and transfers its energy. This leads to the equation for the maximum energy E_max of the emitted electron as
E_max = h ν – φ₀ ; where φ₀ is the work function of the metal. If an electron absorbs 2 photons (each of frequency ν ). What will be the maximum energy for the emitted electron ?

(ii) Why is this fact (two photon absorption) not taken into consideration in our discussion of the stopping potential ?

Q: A particle moves in a closed orbit around the origin, due to a force which is directed towards the origin. The de-Broglie wavelength of the particle varies cyclically between two values λ1 ,  λ2 with λ1> λ2. Which of the following statement are true ?

(a) The particle could be moving in a circular orbit with origin as centre

(b) The particle could be moving in an elliptic orbit with origin as its focus

(c) When the de-Broglie wavelength is  λ1, the particle is nearer the origin than when its value is  λ2

(d) When the de-Broglie wavelength is  λ2 the particle is nearer the origin than when its value is  λ1

Ans: (b) & (d)

Q: Photons absorbed in matter are converted to heat. A source emitting n photon/sec of frequency ν is used to convert 1 kg of ice at 0 °C to water at 0 °C. Then, the time T taken for the conversion

(a) decreases with increasing n, with ν fixed

(b) decreases with n fixed, ν increasing

(c) remains constant with n and ν changing such that n ν = constant

(d) increases when the product n ν  increases

Ans: (a) , (b) & (c)

Q: The de-Broglie wavelength of a photon is twice, the de-Broglie wavelength of an electron. The speed of the electron is v_e = c/100. Then,

(a) E_e/E_{p = 10^-4}

(b) E_e/E_{p = 10^-2}

(c) p_e/(m_{e c) = 10^-2}

(d) p_e/(m_{e c) = 10^-4}

Ans: (b) & (c)

Q: Relativistic corrections become necessary when the expression for the kinetic energy (1/2) mv² , become comparable with mc², where m is the mass of the particle. At what de-Broglie wavelength, will relativistic corrections become important for an electron ?

(a) λ = 10 nm

(b) λ = 10^-1 nm

(c) λ = 10^-4 nm

(d) λ = 10^-6 nm

Ans: (c) & (d)