Suppose that the uncertainty of position of an electron is e

Suppose that the uncertainty of position of an electron is equal to the radius of the n = 1 Bohr orbit for hydrogen. Calculate the simultaneous minimum uncertainty of the corresponding momentum component, and compare this with the magnitude of the momentum of the electron in the n = 1 Bohr orbit.

Solution

The radius of the first bohr orbit is x =0.53×10^-10m. The uncertainty of the its position is equal to this value
xp (1/2).                   ( = h/(2) is reduced Planck constant)

p (1/2) / x

p (1/2)1.0546×10^-34 / 0.53×10^-10

p 9.94×10^-25

momentum of the electron in the first orbit=mv

m= mass of the electron

velocity of electron in the first orbit is v = 2.18x10⁶

P=9.1X10^-31X2.18x10⁶

=1.98X0^-24