With the help of Bohr's theory, how will you determine the kinetic energy of hydrogen or hydrogen-like atoms?

Explanation

Let the no. of positive charges in the nucleus of a given atom or ion be Ze (Z=atomic no. e=charge of a proton). According to Bohr's theory, the electron present in that atom or ion revolves around the nucleus only in stationary orbits.
Let the radius of the stationary orbit be 'r'.
For the stability of the atom, the coulombic force must be equal to the centrifugal force of the electron moving with a velocity 'v' i.e., `(Ze^(2))/(r^(2))=(mv^(2))/(v) or (1)/(2) mv^(2)=(Ze^(2))/(2r)`
`therefore`Kinetic energy of the electron`=(Ze^(2))/(2r)`