Dual Nature of Matter

JEE Main level, single correct, medium

51 of 200

Question 51 of 200

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

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Answer: (C) v2c\dfrac{v}{2c}

λe=λPh{\lambda }_{e}={\lambda }_{Ph}
hpe=hpph\dfrac{h}{{p}_{e}}=\dfrac{h}{{p}_{ph}}
2mke=Ephc\sqrt{2m{k}_{e}}=\dfrac{{E}_{ph}}{c}
2mke=(Eph)2c22m{k}_{e}=\dfrac{{\left({E}_{ph}\right)}^{2}}{{c}^{2}}
keEph=Ephc2(12m)\dfrac{{k}_{e}}{{E}_{ph}}=\dfrac{{E}_{ph}}{{c}^{2}}\left(\dfrac{1}{2m}\right)
=pphc(12m)=\dfrac{{p}_{ph}}{c}\left(\dfrac{1}{2m}\right)
=pec(12m)=\dfrac{{p}_{e}}{c}\left(\dfrac{1}{2m}\right)
=mvc12m=\dfrac{mv}{c}\dfrac{1}{2m}
=v2c=\dfrac{v}{2c}

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