Given `m_(e)=9.11 xx 10^(-31)kg` and `h = 6.626 xx 10^(-34)Js`, the uncertainty involved in the measuremenetof velocity within a distance of `0.1Å` is

Options

A. `5.79xx10^(8)ms^(-1)`
B. `5.79xx10^(5)ms^(-1)`
C. `5.76xx10^(6)ms^(-1)`
D. `5.76xx10^(7)ms^(-1)`

Answer

C

Explanation

According to the given data, `Deltax` is `0.1Å`. Thus, to calculate the uncertainty invelocity, we apply Heisenberg's uncertainty principle:
`(Deltax)(mDeltav_(x))ge(h)/(4pi)`
or `Deltav_(x) ge (h)/(4pim Deltax)`
`ge((6.626xx10^(-34)kg m^(2) s^(-1)))/((4)(3.14)(9.11xx10^(-31)kg)(0.1xx10^(-10)m))`
`ge 0.579 xx 10^(7)ms^(-1)`
`ge 5.79 xx 10^(6)ms^(-1)`