The uncertainty in the position of an electron `(mass = 9.1 xx 10^-28 g)` moving with a velocity of `3.0 xx 10^4 cm s^-1` accurate up to `0.001 %` will be
(Use `(h)/(4 pi)` in the uncertainty expression, where `h = 6.626 xx 10^-27 erg - s`)

Options

A. 1.93 cm
B. 3.84 cm
C. 5.76 cm
D. 7.68 cm

Answer

A

Explanation

(a) According to Heisenberg's uncertainty principle
`Deltax xxDeltav=(h)/(4pim)`
Here, `Deltax=`uncertainty in position
`Delta v`=uncertainty in velocity
h = Planck's constant `(6.626xx10^(-27)Js)`
m = mass of electron `(9.1xx10^(-28) kg)`
Here, `Deltav=0.001%` of `3xx10^(4)`
`=(0.001)/(100)xx3xx10^(4)=0.3cm//s`
`:. Deltax=(h)/(4pi m Delta v)`
`=(6.626xx10^(-27))/(4xx3.14xx9.1xx10^(-28)xx0.3)`=1.93 cm