Uncertainty in the position of an electron `("mass = "9.1 xx 10^(-31)kg)` moving with a velocity `300 ms^(-1)` accurate upto 0.001% will be

Options

A. `19.2xx10^(-2) m`
B. `5.76xx10^(-2) m`
C. `1.92 xx10^(-2) m`
D. `3.84xx10^(-2) m`

Answer

3

Explanation

According to Heisenberg's uncertainity principle
`Deltax xx Deltap=h/(4pi)`
`Deltax xx (m.Deltav)=h/(4pi)rArr Deltax =h/(4pim. Deltav)" "Deltav=0.001/100xx300=3xx10^(-3)ms^(-1)`
`:. Deltax =(6.63xx10^(-34))/(4xx3.14xx9.1xx10^(-31)xx3xx10^(-3))=1.29xx10^(-2)m`.