Question

At what velocity does a electron have a 9 fm wavelength (about the size of a nucleus)? Assume the electron is nonrelativistic. (1 femtometer = 10-15 m ).

Answer 1

Wavelength of the electron, = 9 fm = 9 x 10^-15 m

Mass of an electron, m = 9.109 x 10^-31 kg

Suppose required velocity of the electron = v

Now, use de Broglie equation -

For the wave nature of electron, wavelength of the electron can be defined as -

= h / (m*v)

where, h = plank's constant = 6.626 x 10^-34 J*s

from the above equation, we can write -

v = h / (m*)

= ( 6.626 x 10^-34) / (9.109 x 10^-31 x 9 x 10^-15)

= 8.08 x 10^10 m/s (Answer)