Question

The Mass Of An Electron Is 9.1x10^-31 KG. If it's K.Eis 3.0x10^-25 J. Calculate it's wavelength...(PLEASE SHOW THE WORKING OF FINDING VELOCITY (v)) VERY IMPORTANT!!

Answer 1

Answer : The wavelength of an electron is, $8.99\times 10^{-7}m$

Explanation :

First we have to calculate the velocity of an electron.

Formula used : $K.E=\frac{1}{2}\times mv^2$

where,

K.E = kinetic energy of electron = $3.0\times 10^{-25}J$

m = mass of electron = $9.1\times 10^{-31}Kg$

v = velocity of electron = ?

Now put all the given values in the above formula, we get :

$3.0\times 10^{-25}J=\frac{1}{2}\times (9.1\times 10^{-31}Kg)\times v^2$

By solving the terms, we get

$v=8.1\times 10^{2}m/s$

Now we have to calculate the wavelength of an electron.

Formula used : $\lambda=\frac{h}{mv}$

where,

$\lambda$ = wavelength of electron = ?

h = Planck's constant = $6.626\times 10^{-34}Js$

m = mass of electron = $9.1\times 10^{-31}Kg$

v = velocity of electron = $8.1\times 10^{2}m/s$

Now put all the given values in the above formula, we get :

$\lambda=\frac{6.626\times 10^{-34}Js}{(9.1\times 10^{-31}Kg)\times (8.1\times 10^{2}m/s)}$

$\lambda=8.99\times 10^{-7}m$

Therefore, the wavelength of an electron is, $8.99\times 10^{-7}m$

Answer 2

Since KE = 1/2mv²

v =(2KE/m)² = ( 2×3.0×10^-25 kg m²s-²/9.1×10^-31 kg )½

=812ms-¹

Wavelength = h/mv

= 6.626×10^-34/(9.1×10^-31)(812)

=8967×10^-10

=896.7nm