Question

The mass of an electron is 9.1x10 -31 kg. if its kinetic energy is 3.0x10 -25 J, calculate its wavelength .(h=6.6x10 -34 Js)

Answer 1

Given: 
mass of an electron =  9.1x10 -31 kg
kinetic energy = 3.0x10 -25 J
h=6.6x10 -34 Js

By using de- Broglie equation :
wavelength = h/mv = h/ p  ,where  h = Planck's constant, p= momentum

as P= √2Em , by subtituting the value of p we get,
wavelength = h / √2Em            (E= kinectic energy )
wavelength = 6.6 x 10-34/√2 x 3.0 x 10-25 x 9.1 x 10 -31
                   = 6.6 x 10 -34/√54.6 x 10 - 56
                   = 6.6 x 10 -34/ 7.4 x 10 - 28
                   = 0.89 x 10 -6 m

Answer 2

Answer:

$Required \: weblength \: is \: 0.89 \times {10}^{ - 6} m$

Explanation:

Given,

$mass \: of \: an \: electron \: is \: 9.1 \times {10}^{ - 31} \: kg$

And

$kinetic \: energy \: is \: 3.0 \times {10}^{ - 25} \: jule$

Now we know,

$weblength = \frac{h}{mv} = \frac{h}{p}$

Where h= Planck's constant , p = momentum

[ By rule of De-Brogile equation ]

$P= \sqrt{2} Em$

By subtituting the value of p we get,

$Weblength = \frac{h}{ \sqrt{2}Em}$

$Weblength = \frac{6.6 \times {10}^{ - 34} }{ \sqrt{2}{\times 3 \times {10}^{ - 25} \times 9.1 \times {10}^{ - 31} } }$

$= 0.89 \times {10}^{ - 6} m$

So,

$required \: weblength \: is \: 0.89 \times {10}^{ - 6} m$