Question

A moving electron has 4.55 x 10-25 joules of kinetic energy. Calculate its
wavelength (mass = 9.1 x 10-31 kg and h = 6.626 x 10-34 kg mºs').

Answer 1

$m = 9.1 \times {10}^{ - 31} \: kg$

$h = 6.626 \times {10}^{ - 34} \: kg {m}^{2} {s}^{ - 1}$

$k.e = 4.55 \times {10}^{ - 25} j$

$\frac{1}{2} m {v}^{2} = 4.55 \times {10}^{ - 25}$

${v}^{2} = \frac{4.55 \times {10}^{ - 25} \times 2}{9.1 \times {10}^{ - 3 1} } \\ \\ {v}^{2} = {10}^{6} \\ \\ v = \sqrt{ {10}^{6} } \\ \\ v = {10}^{3} \: m {s}^{ - 1}$

Now,

$\lambda = \frac{h}{mv}$

$\lambda \: = \frac{6.626 \times {10}^{ - 34} }{(9.1 \times {10}^{ - 31} )\times {10}^{3} }$

$\lambda \: = 7.25 \times {10}^{ - 7} m$

So the wavelength is

$7.25 \times {10}^{ - 7} m$