Question

Calculate the kinetic energy of a moving electron which has a wavelength of 4.8 pm

Answer 1

k.e = 1/2 mv²

for v we can use the equation wavelength = h/mv
h is Planck's constant = 6.626 ÷ 10³⁴ joule second
also convert 4.8 picometer into metre = 4.8/10¹²

Answer 2

We know that K.E = 1/2 mv^2             --------------------- (i)

                       v = h/(mlambda)           -------------------- (ii)

Default values are m = 9.1 * 10^-31 kg, h = 6.626 * 10^-34 J

Now Substitute Equation (ii) in (i)

K.E = 1/2 m(h^2/m^2 * lambda ^2)

     On cross multiplication we get

     = h^2/2 * m *  lambda ^ 2               (Given Wavelength(lambda) = 4.8 pm)

     = 6.626 * 10^-34 ^2 / 2 * 9.11 * 10^-31 * (4.8 * 10 ^-12)^2
    
    =  1.052 * 10^-14 J


Hope this helps!