In the Bohr's orbit, what is the ratio of total kinetic energy and total energy of the electron

Options

A. `-1`
B. `-2`
C. `+1`
D. `+2`

Answer

A

Explanation

`K.E. = (1)/(2) mv^(2), P.E. = - (Ze^(2))/(r)`
But electrostatic force = centrifugal force
i.e., `(Ze^(2))/(r^(2)) = (mv^(2))/(r) :. P.E. = - mv^(2)`
Total energy `= (1)/(2) mv^(2) - mv^(2) = - (1)/(2) mv^(2)`
`:.` K.E./Total energy `= -1`
Note. Similarly, `E_("total")//P.E. = 1//2` and K.E./P.E. `= - 1//2`