The uncertainty in the position of an electron `(mass = 9.1 xx 10^-28 g)` moving with a velocity of `3.0 xx 10^4 cm s^-1` accurate up to `0.001 %` will be
(Use `(h)/(4 pi)` in the uncertainty expression, where `h = 6.626 xx 10^-27 erg - s`)

Options

A. 1.93 cm
B. 3.84 cm
C. 5.76 cm
D. 7.68cm

Answer

A

Explanation

Given mass of an electron (m) `=9.1 xx 10^(-28) g,`
Velocity of electron `(v) = 3 xx 106(4) cm//s`
Accuracy in velcoity `= 0.0001 % = (0.001)/(100)`,
Actual velocity of the electron.
`(Deltav) = 3 xx 10^(4) xx (0.001)/(100) = 0.3 cm//s`
Planck.s constant (h) `= 6.626 xx 10^(-27) erg-sec`
`therefore` Uncertainty in the position of the electron .
`(Deltax) = (h)/(4 pi mDelta v) = (6.626 xx 10^(27) xx 7)/(4 xx 22 xx (9.1 xx 10^(-28)) xx 0.3))`
` = 1.93 cm`