MCQ
An electron with speed $v$ and a photon with speed $c$ have the same $de-Broglie$ wavelength. If the kinetic energy and momentum of electron are $E_{ e }$ and $pe _{ e }$ and that of photon are $E _{ ph }$ and $p _{ ph }$ respectively. Which of the following is correct?
  • A
    $\frac{E_{e}}{E_{p h}}=\frac{2 c}{v}$
  • $\frac{E_{e}}{E_{p h}}=\frac{v}{2 c}$
  • C
    $\frac{p_{e}}{p_{p h}}=\frac{2 c}{v}$
  • D
    $\frac{ p _{ e }}{ p _{ ph }}=\frac{ v }{2 c }$

Answer

Correct option: B.
$\frac{E_{e}}{E_{p h}}=\frac{v}{2 c}$
b
$\lambda_{ e }=\lambda_{\text {photon }}$

$\frac{ h }{ mv }=\frac{ h }{ P _{\text {photon}}} \Rightarrow P _{\text {photon }}= mv$

$\frac{ E _{ e }}{ E _{ ph }}=\frac{\frac{1}{2} mv ^{2}}{\frac{ hc }{\lambda}}=\frac{1}{2} \frac{ mv }{ P _{ Ph } C } \times v =\frac{ v }{2 C }$

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