Obtain the mass of an electron in hydrogen atom in terms of its orbital period and radius of orbit.

Explanation

The required centripetal force of the electron in the hydrogen atom is provided by the coulomb force,
`:. (mv^(2))/(r)=(1)/(4pi epsi_(0))(e^(2))/(r^(2))(Z=1)`
`:.(mr^(2) omega^(2))/(r)=(1)/(4pi epsi_(0)) (e^(2))/(r^(2)) ( :. v=romega)`
`:. m omega^(2)=(1)/(4pi epsi_(0))(e^(2))/(r^(3))`
Here taking `omega=(2pi)/(T)`,
`:.m((4pi^(2))/(T^(2)))=(1)/(4pi epsi_(0))(e^(2))/(r^(3))`
`:.m=(e^(2)T^(2))/(16pi^(3)epsi_(0)r^(3))`