A light of wavelength lambda is incident on a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The energy of the incident photon is $E = \frac{hc}{\lambda}$.Since the work function is negligible,the kinetic energy $K$ of the emitted photoele

Vedclass · Accepted Answer

$2 mc : h$

Vedclass · Answer

(C) The energy of the incident photon is $E = \frac{hc}{\lambda}$.Since the work function is negligible,the kinetic energy $K$ of the emitted photoelectron is equal to the energy of the incident photon: $K = \frac{hc}{\lambda}$.The de-Broglie wavelength $\lambda_1$ of the electron is given by $\lambda_1 = \frac{h}{p}$,where $p$ is the momentum of the electron.We know that $K = \frac{p^2}{2m}$,so $p = \sqrt{2mK}$.Substituting $K = \frac{hc}{\lambda}$,we get $p = \sqrt{2m \cdot \frac{hc}{\lambda}}$.Thus,$\lambda_1 = \frac{h}{\sqrt{\frac{2mhc}{\lambda}}}$.Squaring both sides,we get $\lambda_1^2 = \frac{h^2}{\frac{2mhc}{\lambda}} = \frac{h^2 \lambda}{2mhc} = \frac{h \lambda}{2mc}$.Rearranging the terms,we find $\frac{\lambda}{\lambda_1^2} = \frac{2mc}{h}$.Therefore,the ratio $\lambda : \lambda_1^2$ is $2mc : h$.

Similar Questions

$A$ particle is travelling $4$ times as fast as an electron. Assuming the ratio of the de-Broglie wavelength of the particle to that of the electron is $2:1$,the mass of the particle is:

The wavelength $\lambda$ of a photon and the de-Broglie wavelength of an electron have the same value. The ratio of the kinetic energy of the electron to the energy of a photon is ($m=$ mass of electron,$c=$ velocity of light,$h=$ Planck's constant).

An electron accelerated through a potential difference $V_1$ has a de-Broglie wavelength of $\lambda$. When the potential is changed to $V_2$,its de-Broglie wavelength increases by $50 \%$. The value of $\left(\frac{V_1}{V_2}\right)$ is equal to :

$A$ particle of mass $2 \times 10^{-27} \,kg$ has a de-Broglie wavelength of $3.3 \times 10^{-10} \,m$. The kinetic energy of this particle is (Planck's constant $h = 6.6 \times 10^{-34} \,J \cdot s$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module