First slide

Wave nature of matter

Question

If $λ_{0}$ stands for mid-wavelength in the visible region, the de Broglie wavelength for 100 V electrons is nearest to

Moderate

A

$λ_{0} / 5$
B

$λ_{0} / 50$
C

$λ_{0} / 500$
D

$λ_{0} / 5000$

Solution

Order of magnitude calculation is enough.
$\begin{array}{l} λ = \frac{h}{p} = \frac{h}{{(2 m_{e} e V)}^{1 / 2}} = \frac{6.6 \times 10^{- 34} Js}{{(2 \times 9 \times 10^{- 31} \times 100 \times 1.6 \times 10^{- 19})}^{1 / 2}} \approx 10^{- 10} m \end{array}$
Mid-wavelength in visible region is
$\begin{array}{l} λ_{0} \approx 5000 \times 10^{- 10} m \\ Thus, λ = λ_{0} / 5000 \end{array}$

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