Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Dual Nature of Radiation question

2021 · 27 Jul · Shift 1 · Q69
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.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Dual Nature of Radiation
  5. /2021 · 27 Jul · Shift 1 · Q69

Dual Nature of Radiation question

2021 · 27 Jul · Shift 1 · Q69

JEE MainPhysicsDual Nature of RadiationNumerical+4 / −1
A particle of mass 9.1 ×\times× 10 −-− 31 kg travels in a medium with a speed of 106 m/s and a photon of a radiation of linear momentum 10 −-− 27 kg m/s travels in vacuum. The wavelength of photon is ‾\underline{\hspace{2cm}}​ times the wavelength of the particle.
Numerical answer
View written solutionFree

Correct answer: 910

  1. Wavelength of the particle (de Broglie wavelength)

For a particle of mass mmm moving with speed vvv, the de Broglie wavelength is

λp=hmv\lambda_p = \frac{h}{mv}λp​=mvh​

Given:

  • m=9.1×10−31 kgm = 9.1 \times 10^{-31}\ \text{kg}m=9.1×10−31 kg
  • v=106 m/sv = 10^6\ \text{m/s}v=106 m/s

So momentum of the particle is

pp=mv=9.1×10−31×106=9.1×10−25 kg m/sp_p = mv = 9.1 \times 10^{-31} \times 10^6 = 9.1 \times 10^{-25}\ \text{kg m/s}pp​=mv=9.1×10−31×106=9.1×10−25 kg m/s

Hence,

λp=h9.1×10−25\lambda_p = \frac{h}{9.1 \times 10^{-25}}λp​=9.1×10−25h​

  1. Wavelength of the photon

For a photon,

λγ=hpγ\lambda_{\gamma} = \frac{h}{p_{\gamma}}λγ​=pγ​h​

Given photon momentum:

pγ=10−27 kg m/sp_{\gamma} = 10^{-27}\ \text{kg m/s}pγ​=10−27 kg m/s

Thus,

λγ=h10−27\lambda_{\gamma} = \frac{h}{10^{-27}}λγ​=10−27h​

  1. Find how many times the photon wavelength is the particle wavelength

We need

λγλp=h/10−27h/(9.1×10−25)\frac{\lambda_{\gamma}}{\lambda_p} = \frac{h/10^{-27}}{h/(9.1 \times 10^{-25})}λp​λγ​​=h/(9.1×10−25)h/10−27​

The Planck constant hhh cancels:

λγλp=9.1×10−2510−27\frac{\lambda_{\gamma}}{\lambda_p} = \frac{9.1 \times 10^{-25}}{10^{-27}}λp​λγ​​=10−279.1×10−25​

=9.1×102=910= 9.1 \times 10^2 = 910=9.1×102=910

  1. Final answer

The wavelength of the photon is

910\boxed{910}910​

times the wavelength of the particle.

PreviousNext

More from Dual Nature of Radiation

  • An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV. The proton captures the electron and forms a hydrogen atom in second excited state. The resulting photon is incident on…2021 · MCQ
  • A moving proton and electron have the same de-Broglie wavelength. If K and P denote the K.E. and momentum respectively. Then choose the correct option :2021 · MCQ
  • A free electron of 2.6 eV energy collides with a H+ ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon. (h = 6.6 × 10 − 34 Js)2021 · MCQ
  • Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is…2021 · MCQ
  • When radiation of wavelength λ is used to illuminate a metallic surface, the stopping potential is V. When the same surface is illuminated with radiation of wavelength 3 λ, the stopping potential is 4V​. If the…2020 · Numerical
  • A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is 1.878 × 10–4. The mass of the particle is close to2020 · MCQ
  • When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to :2020 · MCQ
  • Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500 nm, respectively. Both the sources emit light of the same power 200 W. The ratio of the number density of photons of X-rays to the number density of…2020 · MCQ