Answer: 2.068*[tex]10^{-14}[/tex]m
Explanation: According to work energy-theorem , the workdone in accelerating the electron equals the energy it would give off in terms of light.
workdone= qV
energy = hc/λ
q=magnitude of an electronic charge= 1.602*[tex]10^{-16}[/tex]
h= planck constant = 6.626*[tex]10^{-34}[/tex]
c= speed of light =2.998* [tex]10^{8}[/tex]
v= potential difference= 6*[tex]10^{4}[/tex]
λ= wavelength=unknown
by making λ subject of formulae we have that
λ= [tex]\frac{hc}{qv}[/tex]
λ = 6.626*[tex]10^{-34}[/tex] * 2.998* [tex]10^{8}[/tex] / 1.602*[tex]10^{-16}[/tex] * 6*[tex]10^{4}[/tex]
λ = [tex]\frac{19.878*10^{-26} }{9.612*10^{-12} }[/tex]
by doing the necessary calculations, we have that
λ = 2.068*[tex]10^{-14}[/tex]m