A proton of mass '' has same energy as that of a photon of wavelength ''. If the proton is moving at non-relativistic speed, then ratio of its de-Broglie wavelength to the wavelength of photon is. [2025]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
A proton of mass ' $m_{p}$ ' has same energy as that of a photon of wavelength ' $λ$ '. If the proton is moving at non-relativistic speed, then ratio of its de-Broglie wavelength to the wavelength of photon is. [2025]

1 $\frac{1}{c} \sqrt{\frac{2 E}{m_{p}}}$

2 $\frac{1}{c} \sqrt{\frac{E}{m_{p}}}$

3 $\frac{1}{c} \sqrt{\frac{E}{2 m_{p}}}$

4 $\frac{1}{2 c} \sqrt{\frac{E}{m_{p}}}$

Ans.
(3)

E is missing in the question but considering E as energy.

Energy of photon, $E_{photon} = \frac{h c}{λ_{photon}}$

$\Rightarrow$ Wavelength of photon, $λ_{photon} = \frac{h c}{E}$

Energy of proton, $E_{proton} = \frac{1}{2} m_{p} v^{2} = \frac{p^{2}}{2 m_{p}}$

$\Rightarrow$ Linear momentum of proton, $p = \sqrt{2 m_{p} E}$

or de-Broglie wavelength of proton, $λ_{proton} = \frac{h}{p} = \frac{h}{\sqrt{2 m_{p} E}}$

Ratio $\frac{λ_{proton}}{λ_{photon}} = \frac{h}{\sqrt{2 m_{p} E}} \times \frac{E}{h c} = \frac{1}{c} \sqrt{\frac{E}{2 m_{p}}}$

Want Us to Email you About Special Offers & Updates?