A proton of mass m_p has the same energy as t | vedclass

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

Question

(C) Let the energy of both the proton and the photon be $E$.For the photon,the energy is given by $E = \frac{hc}{\lambda_{photon}}$,so $\lambda_{photo

Vedclass · Accepted Answer

$\frac{1}{c} \sqrt{\frac{E}{2 m_p}}$

Vedclass · Answer

(C) Let the energy of both the proton and the photon be $E$.For the photon,the energy is given by $E = \frac{hc}{\lambda_{photon}}$,so $\lambda_{photon} = \frac{hc}{E}$.For the proton,the kinetic energy is $E = \frac{1}{2} m_p v^2$. The momentum of the proton is $p = \sqrt{2 m_p E}$.The de Broglie wavelength of the proton is $\lambda_{proton} = \frac{h}{p} = \frac{h}{\sqrt{2 m_p E}}$.The ratio of the de Broglie wavelength of the proton to the wavelength of the photon is:$\frac{\lambda_{proton}}{\lambda_{photon}} = \frac{h / \sqrt{2 m_p E}}{hc / E} = \frac{h}{\sqrt{2 m_p E}} 	imes \frac{E}{hc} = \frac{E}{c \sqrt{2 m_p E}} = \frac{1}{c} \sqrt{\frac{E}{2 m_p}}$.

$A$ proton of mass $m_p$ has the same energy as that of a photon of wavelength $\lambda$. If the proton is moving at non-relativistic speed,then the ratio of its de Broglie wavelength to the wavelength of the photon is:

Similar Questions

If the de Broglie wavelength of an electron is $5200 \ \mathring{A}$,what is its velocity?

$A$ particle $A$ of mass $m$ and initial velocity $v$ collides with a particle $B$ of mass $\frac{m}{2}$ which is at rest. The collision is head-on and elastic. The ratio of the de-Broglie wavelengths $\lambda_A$ and $\lambda_B$ after the collision is

Proton $(P)$ and electron $(e)$ will have the same de Broglie wavelength when the ratio of their momentum is (assume,$m_{p} = 1849 \, m_{e}$)

Find the de Broglie wavelength of an electron in a metal at $27^{\circ}C$.

An electron of mass $m$ with an initial velocity $\vec{V} = V_0 \hat{i} \,(V_0 > 0)$ enters an electric field $\vec{E} = -E_0 \hat{i} \,(E_0 = \text{constant} > 0)$ at $t = 0$. If $\lambda_0$ is its de-Broglie wavelength initially,then its de-Broglie wavelength at time $t$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module