Find the initial momentum of electron if the momentum of electron is changed by $P m$ and the de Broglie wavelegth associated with it changes by $0.50$ %.

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Solution

By De-Broglie equation,
$λ = h / m v = h / P_{m}$ ..(1)
$P$ is the initial momentum of electron and $P_{m}$ be the decrease in momentum of electron, when wavelength of electron change by $0.50$ %
$λ + 0.5 λ / 100 = h / (P - P_{m})$
$100.5 λ / 100 = h / (P - P_{m})$ ..(2)
By eq (1) and (2),
$P = 1.99 P_{m}$
$∴$ Initial momentumof electron is $1.99 P_{m}$

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Find the initial momentum of electron if the momentum of electron is changed by Pm and the de Broglie wavelegth associated with it changes by 0.50%.

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Find the initial momentum of electron if the momentum of electron is changed by $P m$ and the de Broglie wavelegth associated with it changes by $0.50$ %.