Consider `3rd` orbit of `He^(+)` (Helium) using nonrelativistic approach the speed of electron in this orbit will be (given `K = 9 xx 10^(9)` constant `Z = 2` and `h` (Planck's constant) `= 6.6 xx 10^(-34)Js`.)

Options

A. `0.73xx10^(6)m//s`
B. `3.0xx10^(8)m//s`
C. `2.92xx10^(6)m//s`
D. `1.46xx10^(6)m//s`

Explanation

Energy of electron in `He^(+)3^("rd")` orbit
`E_(3)=-13.6xx(Z^(2))/(n^(2))eV=-13.6xx(4)/(9)eV`
`=-13.6xx(4)/(9)xx1.6xx10^(-19)J~=9.7xx10^(-19)J`
As per Bohr.s model,
Kinetic energy of electron in the `3^("rd")` orbit `=-E_(3)`
`therefore" "9.7xx10^(-19)=(1)/(2)m_(e)v^(2)`
`v=sqrt((2xx9.7xx10^(-19))/(9.1xx10^(-31)))=1.46xx10^(6)ms^(-1)`