Question

The uncertainties in the position and velocity of a particle are 9.54 x 10-10 m and 5.5 x
10-20 ms-1, respectively. Calculate the mass of particle (h = 6.6 x 10-34 kg mạ8-?)​

Answer 1

According to Heisenberg uncertainty principle,

Δx.Δρ = h/4π
(ρ = mν)
Therefore,
Δx.Δνm = h/4π
Δx.Δν = h/4πm

Given:

Δx ( uncertainty in position) = 9.54 x 10^-10 m

Δν ( uncertainty in velocity) = 5.5 x 10^-20 m/s


Δx.Δν = h/4πm

(9.54 x 10^-10) (5.5 x 10^-20) = 6.6 x 10^-34 / ( 4 x 3.14 x m)

52.47 x 10^-30 = 6.6 x 10^-34 / ( 4 x 3.14 x m)

4 x 3.14 x m = 6.6 x 10^-34 / 52.47 x 10^-30

m = 6.6 x 10^-34 / (52.47 x 10^-30 x 4 x 3.14)

m = ( 6.6 / 659 ) x 10^-4

m = 0.01001517 x 10^-4

m = 0.000001

m = 10^-6 kg