The wavelengths of electron waves in two orbits is 3:5. The ratio of kinetic energy of electrons will be

Options

A. `25:9`
B. `5:3`
C. `9:25`
D. `3:5`

Answer

A

Explanation

`K.E.=1/2mv^(2)`
But `lamda=h//mv`
`rArrv=h/(mlamda)`
So, K.E. = `1/2m(h/(mlamda))^(2)`
`K.E.=h^(2)/(2mlamda^(2))orK.E.prop1/lamda^(2)`
`KE_(1)=(h^(2)/(2m))1/((3lamda)^(2))`
`KE_(2)=(h^(2)/(2m))1/((5lamda)^(2))`
`KE_(1):KE_(2)=25:9`.