If an electron is revolving around the hydrogen nucleus at a distance 0.1 mm. What should be its speed

Options

A. `2.188xx10^(6)ms^(-1)`
B. `1.094xx10^(6)ms^(-1)`
C. `4.376xx10^(6)ms^(-1)`
D. `1.59xx10^(6)ms^(-1)`

Answer

D

Explanation

Electrostatic force=centripetal force
`(1)/(4piepsi_(0))(Ze^(2))/(r^(2))=(mv^(2))/(r)`
`therefore v=sqrt(((1)/(4piepsi_(0))(Ze^(2))/(mr)))`
`=sqrt((9xx10^(9)xx1xx(1.6xx10^(-19))^(2))/((9.1xx10^(-31))xx(0.1xx10^(-9)))`
`=1.59xx10^(6)ms^(-1)`