If an electron is revolving around the hydrogen nucleus at a distance of 0.1 nm,what should be its speed?

Options

A. ` 2.188 xx 10^(6) ms^(-1)`
B. `1.094 xx 10^(6) ms^(-1)`
C. `4.376 xx 10^(6) ms^(-1)`
D. `1.529 xx 10^(6) ms^(-1)`

Answer

D

Explanation

Electrostatic force = centripetal force
`(1)/( 4pi epsi_(0))(Ze^(2))/(r^(2))=(mv^(2))/(r)`
` :. V=sqrt(((1)/( 4 pi epsi_(0))(Ze^(2))/(mr)))`
`= sqrt((9 xx 10^(9) xx 1 xx(1.6 xx 10^(-19))^(2))/((9.1xx10^(-31))xx(0.1 xx 10^(-9))))=1.59xx10^(6) ms^(-1)`