The de Broglie wavelength of electron accelerated through $V$ volt is nearly given by:
$λ (i n ˚ A) = {[\frac{x}{V}]}^{1 / 2}$ . Find the value of $\frac{x}{75}$ .

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Solution

De Broglie's wavelngth of electron $λ$ is:
$λ = \frac{h}{m u} = \frac{h}{\sqrt{2 e . V . m}}$ $(∵ e V = 1 / 2 m u^{2})$
$= \frac{6.626 \times 10^{- 34}}{\sqrt{2 \times 1.6 \times 10^{- 19} \times V \times 9.1 \times 10^{- 31}}}$
$= \frac{6.626 \times 10^{- 34}}{5.396 \times 10^{- 25} [V]^{1 / 2}} = \frac{1.227 \times 10^{- 9}}{[V]^{1 / 2}}$ metre
$= \frac{12.27 \times 10^{- 10}}{[V]^{1 / 2}}$ metre $= \frac{12.27}{[V]^{1 / 2}} A^{o} = {[\frac{150}{V}]}^{1 / 2} A^{o}$

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The de Broglie wavelength of electron accelerated through V volt is nearly given by:λ(in ˚A)=[xV]1/2. Find the value of x75.

De Broglie's wavelngth of electron λ is:λ=hmu=h√2e.V.m (∵eV=1/2mu2)=6.626×10−34√2×1.6×10−19×V×9.1×10−31=6.626×10−345.396×10−25[V]1/2=1.227×10−9[V]1/2 metre=12.27×10−10[V]1/2 metre=12.27[V]1/2Ao=[150V]1/2Ao

The de Broglie wavelength of electron accelerated through $V$ volt is nearly given by:
$λ (i n ˚ A) = {[\frac{x}{V}]}^{1 / 2}$ . Find the value of $\frac{x}{75}$ .