Dual Nature of Radiation and Matter — Class 12 Physics PYQs

The stopping potential $V_0$ measured in a photoelectric experiment for a metal surface is plotted against frequency v of the incident radiation. Let m be the slope of the straight line so obtained. Then the value of charge of an electron is given by (h is the Planck's constant.)
(A) mh
(B) $\frac{m}{h}$
(C) $\frac{h}{m}$
(D) $\frac{1}{mh}$

In a photoelectric experiment with a material of work function 2.1 eV, the stopping potential is found to be 2.5 V. The maximum kinetic energy of ejected photoelectrons is
(A) 0.4 eV
(B) 2.1 eV
(C) 2.5 eV
(D) 4.6 eV

Let ${\lambda }_e,{\lambda }_p$ and ${\lambda }_d$ be the wavelengths associated with an electron, a proton and a deuteron, all moving with the same speed. Then the correct relation between them is
(A) ${\lambda }_d>{\lambda }_p>{\lambda }_e$
(B) ${\lambda }_e>{\lambda }_p>{\lambda }_d$
(C) ${\lambda }_p>{\lambda }_e>{\lambda }_d$
(D) ${\lambda }_e={\lambda }_p={\lambda }_d$

A light of wavelength 400 nm is incident on metal surface whose work function is $3.0\times 10^{-19}$ J. Calculate the speed of the fastest photoelectrons emitted.

The threshold wavelength of a metal is 450 nm. Calculate (i) the work function of the metal in eV and (ii) the maximum energy of the ejected photoelectrons in eV by incident radiation of 250 nm.

Draw a plot of frequency v of incident radiations as a function of stopping potential $V_0$ for a given photo emissive material. What information can be obtained from the value of the intercept on the stopping potential axis ?
(b) Calculate : (i) the momentum and (ii) de Broglie wavelength, of an electron with kinetic energy of 80 eV.

The momentum (in SI units) associated with a photon of energy 1.5 eV is :
(A) 4 × 10${}^{-27}$
(B) 8 × 10${}^{-28}$
(C) 2 × 10${}^{-30}$
(D) 6 × 10${}^{-29}$

Two beams, A and B whose photon energies are 3.3 eV and 11.3 eV respectively, illuminate a metallic surface (work function 2.3 eV) successively. The ratio of maximum speed of electrons emitted due to beam A to that due to beam B is :
(A) 3
(B) 9
(C) 1/3
(D) 1/9

The waves associated with a moving electron and a moving proton have the same wavelength $\lambda$. It implies that they have the same :
(A) momentum
(B) angular momentum
(C) speed
(D) energy

Assertion (A) : In photoelectric effect, the kinetic energy of the emitted photoelectrons increases with increase in the intensity of the incident light.
Reason (R) : Photoelectric current depends on the wavelength of the incident light.