In an atom , an electron is moving with a speed of 600 m/s with an accuracy of `0.05%` . The certainty with which the position of the electron can be located is (h = `6.6 xx 10^(-34) kgm^(2)s^(-1)` , mass of electron , `e_(m) = 9.1 xx 10^(-31)` kg ):

Options

A. `1.52 xx 10^(-4) m`
B. `5.10 xx 10^(-3) m`
C. `1.92 xx 10^(-3)m`
D. `3.84 xx 10^(-3) m`

Answer

C

Explanation

`Delta v = (0.005)/(100) xx 600 ms^(-1) = 3 xx 10^(-2) ms^(-1)`
`Delta x xx m Delta v = (h)/(4pi)`
`:. Delta x = (h)/(4pi m Delta v)`
`= (6.6 xx 10^(-34) kg m^(2) s^(-1))/(4 xx 3.14 xx 9.1 xx 10^(-31) kg xx 3 xx 10^(-2) ms^(-1))`
`= 1.92 xx 10^(-3) m`