An electron of mass m and charge e moves from point A to point C which are respectively at potentials of `+5V` and `-4V`. The electron will acquire the wavelength of

Options

A. `(2h)/(sqrt(3em))`
B. `(h)/(sqrt(18" em"))`
C. `(h^(2))/(sqrt(5"em"))`
D. `(2h)/(sqrt(7" em"))`

Answer

B

Explanation

Potential difference is given by
`V=V_(1)-V_(2)=5-(-4)=9V`
Now, KE gained by the electron is
`=(1)/(2)mv^(2)=eV=9e`
So, `" "v=sqrt((18e)/(m))`
`:.` Wavelength of the electron
`lambda_(e)=(h)/(mv)=(h)/(msqrt((18e)/(m)))=(h)/(sqrt(18em))`