New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Dual Nature of Radiation question

2022 · 24 Jun · Shift 2 · Q62

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Main
Physics
Dual Nature of Radiation
2022 · 24 Jun · Shift 2 · Q62

Dual Nature of Radiation question

2022 · 24 Jun · Shift 2 · Q62

JEE MainPhysicsDual Nature of RadiationMCQ+4 / −1

The light of two different frequencies whose photons have energies 3.8 eV and 1.4 eV respectively, illuminate a metallic surface whose work function is 0.6 eV successively. The ratio of maximum speeds of emitted electrons for the two frequencies respectively will be :

A
1 : 1
B
2 : 1
C
4 : 1
D
1 : 4

View written solutionFree

Correct answer: B

Use Einstein’s photoelectric equation

For photoelectric emission, $K_{\max} = h\nu - \phi$ where:

$K_{\max}$ = maximum kinetic energy of emitted electron
$h\nu$ = photon energy
$\phi$ = work function

Given work function: $\phi = 0.6\,\text{eV}$

Photon energies are:

First light: $3.8\,\text{eV}$
Second light: $1.4\,\text{eV}$

Find maximum kinetic energies

For the first frequency: $K_1 = 3.8 - 0.6 = 3.2\,\text{eV}$

For the second frequency: $K_2 = 1.4 - 0.6 = 0.8\,\text{eV}$

Relate kinetic energy to speed

Since $K_{\max} = \frac{1}{2}mv^2$ for electrons of the same mass, $v \propto \sqrt{K}$

Therefore, $\frac{v_1}{v_2} = \sqrt{\frac{K_1}{K_2}} = \sqrt{\frac{3.2}{0.8}} = \sqrt{4} = 2$

So the ratio of maximum speeds is: $v_1 : v_2 = 2 : 1$

Check options

A: $1:1$ ❌
B: $2:1$ ✅
C: $4:1$ ❌
D: $1:4$ ❌

Hence, the correct option is B.

More from Dual Nature of Radiation

A metal exposed to light of wavelength $500 nm$ and and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength $500 nm$ is used. The…2022 · MCQ
The ratio of wavelengths of proton and deuteron accelerated by potential Vp and Vd is 1 : $2$ . Then the ratio of Vp to Vd will be :2022 · MCQ
A proton, a neutron, an electron and an $α$ particle have same energy. If $λ$ p, $λ$ n, $λ$ e and $λ$ a are the de Broglie's wavelengths of proton, neutron, electron and $α$ particle respectively, then…2022 · MCQ
A parallel beam of light of wavelength $100 Wm^{- 2}$ and intensity $100 Wm^{- 2}$ is incident on a surface perpendicular to the beam. The number of photons crossing $1 cm^{2}$ area perpendicular to the beam in one…2022 · MCQ
An electron with speed v and a photon with speed c have the same de-Broglie wavelength. If the kinetic energy and momentum of electron are Ee and pe and that of photon are Eph and pph respectively. Which of the following is correct?2022 · MCQ
A metal surface is illuminated by a radiation of wavelength 4500 $A o$ . The ejected photo-electron enters a constant magnetic field of 2 mT making an angle of 90 $^{\circ}$ with the magnetic field. If it starts revolving in a…2022 · MCQ
The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength 6630 $A o$ is 0.42 V. If the threshold frequency is x $\times$ 1013 /s, where x is (nearest…2022 · Numerical
An electron (mass $m$ ) with an initial velocity $v = v_{0} \hat{i} (v_{0} > 0)$ is moving in an electric field $E = - E_{0} \hat{i} (E_{0} > 0)$ where $E_{0}$ is constant. If at $t = 0$ de…2022 · MCQ