If the momentum of electron is changed by P then the de Broglie wavelength associated with it changes by 1%. The initial momentum of electron will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 100 P
The De-Broglie wavelength (λ) is,
$λ=\frac{h}{P}$
∴ Change in wavelength after momentum change ΔP.
$λ'=\frac{h}{P+ΔP}$
∴ Change in wavelength,
$Δλ=λ-λ'=\frac{h}{P}-\frac{h}{P+ΔP}$
$=\frac{h}{P}\left(1-\frac{1}{1+\frac{ΔP}{P}}\right)$
$Δλ≃\frac{h}{P}×\frac{ΔP}{P}$
$⇒\frac{Δλ}{λ}=\frac{ΔP}{P}=0.01$
$⇒P=\frac{ΔP}{0.01}=100P$ $[ΔP=P]$
∴ The initial momentum is 100 P.