the suitable photon is employed to locate an (mass `=9.11 xx 10^(-31) kg)` in an atom which distance of 10.98 nm the ungranintly involved in the measurement of its velocity in `ms^(-1)` is

Options

A. `(1.565 xx 10^(6))/(pi)`
B. `(1.6565 xx 10^(4))/(pi)`
C. `(1.6565 xx 10^(-8))/(pi)`
D. `(1.6565 xx 10^(8))/(pi)`

Answer

B

Explanation

Given
mass of electron = `9.1 xx 10^(11) kg `
Position of electron `=10.98 nm`
`=10.98 xx 10^(-9) m`
Here planck constant `=6.63 xx 10^(34) js`
According to Heisenberg uncertainty
`Delta x .Delta x = (h )/( 4pi m)`
`:. Delta v = (6.63 xx 10^(-34))/( 4xx pi xx 9.11 xx 10^(-11 ) kg xx 10.98 xx 10^(9) m)`
`Delta v = (1.656 xx 10^(4))/( pi )`
`Delta v= ` uncertainty in velocity of electron