NCERT Solutions for Chapter: Dual Nature of Radiation and Matter, Exercise 4: LA

Consider an electron in front of metallic surface at a distance $d$ (treated as an infinite plane surface). Assume the force of attraction by the plate is given as $\frac{1}{4}\frac{q^2}{4\pi {\epsilon }_0{d}^2}$. Calculate work in taking the charge to an infinite distance from the plate. Taking $d=0.1\mathrm{nm}$, find the work done in electron volts. [Such a force law is not valid for $d<0.1 \mathrm{nm}$].

A student performs on experiment on photoelectric effect, using two materials A and B. A plot of $V_{stop}$ vs $\nu$  is given in figure.

Which material A or B has a higher work function?

A student performs on experiment on photoelectric effect, using two materials A and B. A plot of $V_{stop}$ vs $\nu$ is given in figure.

Given the electric charge of an electron $=1.6\times {10}^{-19}\mathrm{C}$, find the value of $h$ obtained from the experiment for both A and B.

Comment on whether it is consistent with Einstein's theory:

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.

Consider a $20 \mathrm{W}$ bulb emitting light of wavelength $5000Å$ and shining on a metal surface kept at a distance $2 \mathrm{m}$. Assume that the metal surface has work function of $2 \mathrm{eV}$ and that each atom on the metal surface can be treated as a circular disk of radius $1.5Å$.
Will there be photoelectric emission?

Consider a $20 \mathrm{W}$ bulb emitting light of wavelength $5000Å$ and shining on a metal surface kept at a distance $2 \mathrm{m}$. Assume that the metal surface has work function of $2 \mathrm{eV}$ and that each atom on the metal surface can be treated as a circular disk of radius $1.5Å$.
How much time would be required by the atomic disk to receive energy equal to work function $(2 \mathrm{eV})$?

Consider a $20 \mathrm{W}$ bulb emitting light of wavelength $5000Å$ and shining on a metal surface kept at a distance $2 \mathrm{m}$. Assume that the metal surface has work function of $2 \mathrm{eV}$ and that each atom on the metal surface can be treated as a circular disk of radius $1.5Å$. How many photons would atomic disk receive within time duration $11.4 s ?$

Use No.of photon emitted by bulb per second is $n_1=5\times {10}^{19}$

Consider a $20 \mathrm{W}$ bulb emitting light of wavelength $5000Å$ and shining on a metal surface kept at a distance $2 \mathrm{m}$. Assume that the metal surface has work function of $2 \mathrm{eV}$ and that each atom on the metal surface can be treated as a circular disk of radius $1.5Å$.
Can you explain how photoelectric effect was observed instantaneously,?

Given Time of emission of electrons is $11.4 s.$