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11.Dual Nature of Radiation and matter
medium
An electron and a photon have same wavelength of $10^{-9} \,m$. If $E$ is the energy of the photon and $p$ is the momentum of the electron, then the magnitude of $E / p$ (in $SI$ unit) is
A
$1.00 \times 10^{-9}$
B
$1.50 \times 10^8$
C
$3.00 \times 10^8$
D
$1.20 \times 10^7$
(KVPY-2016)
Solution
$(c)$ For a photon energy is
$E=h f=\frac{h c}{\lambda}$
For an momentum of electron is $p=\frac{h}{\lambda}$
So, $\frac{E}{p}=\frac{h c / \lambda}{h / \lambda}=c$
here, $\lambda$ is same for both photon and electron.
$\Rightarrow \quad \frac{E}{p}=3 \times 10^8 \,ms ^{-1}$
Standard 12
Physics
