Calculate the uncertainty in position of an electron whose velocity is `3.0 xx 10^4 cms^(-1)` accurate up to 0.001%. Mass of an electron `=9.1 xx 10^(-28)g`.

Options

A. `1.52xx10^(-4)m`
B. `5.10xx10^(-3)m`
C. `1.92xx10^(-3)`
D. `3.84xx10^(-3)m`

Answer

C

Explanation

Given, velocity of `e^(-), v=600ms^(-1)`
Accuracy of velocity `=0.005%" "therefore" "Deltav=(600xx0.005)/(100)=0.03`
According to Heisenberg’s uncertainty principle,
`Deltax. mDelta ge (h)/(4pi)" "rArr" "Deltax=(6.6xx10^(-34))/(4xx3.14xx9.1xx10^(-31)xx0.03)=1.92xx10^(-3)m`