Question

If an electron in a quantum well is confined to an area that is 470 nm wide, what is the uncertainty in the electron’s velocity along the same direction?

Answer 1

given,
(delta x) = 470 nm
= (470*10^-9) m

use,
m*(delta v) = h/{4*3.14*(delta x)}
where,
m = mass of electron
= (9.1*10^-31) kg
h = planck constant
= (6.63*10^-34) J.s

so,
m*(delta v) = h/{4*3.14*(delta x)}
(9.1*10^-31)*(delta v) = (6.63*10^-34)/{4*3.14*(470*10^-9)}
(9.1*10^-31)*(delta v) = (6.63*10^-34)/(5.9032*10^-6)
(9.1*10^-31)*(delta v) = (1.123*10^-28)
delta v = 123.4 m/s

Answer: 123.4 m/s

Answer 2

given,
(delta x) = 470 nm
= (470*10^-9) m

use,
m*(delta v) = h/{4*3.14*(delta x)}
where,
m = mass of electron
= (9.1*10^-31) kg
h = planck constant
= (6.63*10^-34) J.s

so,
m*(delta v) = h/{4*3.14*(delta x)}
(9.1*10^-31)*(delta v) = (6.63*10^-34)/{4*3.14*(470*10^-9)}
(9.1*10^-31)*(delta v) = (6.63*10^-34)/(5.9032*10^-6)
(9.1*10^-31)*(delta v) = (1.123*10^-28)
delta v = 123.4 m/s

Answer: 123.4 m/s