The uncertainty in the velocity of a particle of mass `6.626 xx 10^(-31) kg` is `1 xx 10^6 ms^(-1)`. What is the uncertainty in its position (in nm) ? `(h = 6.626 xx 10^(-34) Js)`

Options

A. `(1)/(2pi)`
B. `(2.5)/(pi)`
C. `(4)/(pi)`
D. `(1)/(4pi)`

Answer

D

Explanation

According to Heisenberg.s uncertainty principle
`m Deltav xx Delta x ge (h)/(4pi)`
`m=6.626xx10^(-28)kg`
`Deltav=10^(-6) m//sec`
`h=6.626xx10^(-34)Js`
`6.626 xx10^(-28)xx10^(-6) xx Delta x =(6.626 xx 10^(-34))/(4pi)`
`Delta x = (6.626xx 10^(-34))/(4pi xx 6.626xx10^(-34))=(1)/(4pi)`