In an atom, an electron is moving with a speed of ` 600 m//s` with an accuracy of ` 0.005%` . Certainty with which the position of the electron can be localized is :
` ( h = 6.6 xx 10^(-34) kg m^2 s^(-1)` ,
mass of electron ` (e_m) = 9. 1 xx10^(-31) kg)`.

Options

A. `1.52 xx 10^(-4)m`
B. `5 xx 10 xx 10^(-3)m`
C. `1.92 xx 10^(-3)m`
D. `3.84 xx 10^(-3)m`

Answer

C

Explanation

By Heisenberg.s uncertainty principle, `Delta m Delta v=(h)/(4pi)`
`Delta v= 0.005% or 600 m//s`
`=(600 xx 0.005)/(100)= 0.03`
`Delta x= 9.1 xx 10^(-31) xx 0.03=(6.6 xx 10^(-34))/(4 xx 3.14)`
Hence, `Delta x= (6.6 xx 10^(-34))/(4 xx 3.14 xx 0.03 xx 9.1 xx 10^(-31))= 1.92 xx 10^(-3)m`