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. `1.92xx10^(-2)m`
D. `3.84xx10^(-2)m`

Answer

C

Explanation

According to Heisenberg’s uncertainty principle,
`Delta x xx Deltap=(h)/(4pi)" "Deltax. (m. Deltav)=(h)/(4pi) rArr Deltax =(h)/(4pim.Deltav)`
Here `Deltav=(0.001)/(100)xx300=3xx10^(-3) ms^(-1)`
`therefore" "Detalx=(6.63xx10^(-34))/(4xx3.14xx9.1xx10^(-31)xx3xx10^(-3))=1.92xx10^(-2)m`