Verified Solution • 2025–26 Session moderate

QJEEM21Ph11dc: JEE Main 2021 Physics - Class 12 JEEM21Ph11dc Solution: An electron moving with speed v and a photon moving with speed…

An electron moving with speed v and a photon moving with speed c, have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is :

Multiple Choice Options

  • A 3cv{{3c} \over v}
  • B v3c{v \over {3c}}
  • C v2c{v \over {2c}}
  • D 2cv{{2c} \over v}

Step-by-Step Verified Solution

λe=λPh{\lambda _e} = {\lambda _{Ph}}

hpe=hpph{h \over {{p_e}}} = {h \over {{p_{ph}}}}

2mke=Ephc\sqrt {2m{k_e}} = {{{E_{ph}}} \over c}

2mke=(Eph)2c22m{k_e} = {{{{({E_{ph}})}^2}} \over {{c^2}}}

keEph=Ephc2(12m){{{k_e}} \over {{E_{ph}}}} = {{{E_{ph}}} \over {{c^2}}}\left( {{1 \over {2m}}} \right)

=pphc(12m)= {{{p_{ph}}} \over c}\left( {{1 \over {2m}}} \right)

=pec(12m)= {{{p_e}} \over c}\left( {{1 \over {2m}}} \right)

=mvc12m= {{mv} \over c}{1 \over {2m}}

=v2c= {v \over {2c}}

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