Answer: 459 nm
Explanation:
The relation between energy and wavelength of light is given by Planck's equation, which is:
[tex]E=\frac{Nhc}{\lambda}[/tex]
where,
E = energy of the light = [tex]261 kJ=261000J[/tex] (1kJ=1000J)
N= avogadro's number = [tex]6.023\times 10^{23}[/tex]
h = Planck's constant = [tex]6.626\times 10^{-34}Js[/tex]
c = speed of light = [tex]3\times 10^8m/s[/tex]
[tex]\lambda[/tex] = wavelength of light = ?
Putting the values in the equation:
[tex]261000J=\frac{6.023\times 10^{23}\times 6.626\times 10^{-34}Js\times 3\times 10^8m/s}{\lambda}[/tex]
[tex]\lambda=4.587\times 10^{-7}m=459nm[/tex] [tex]1nm=10^{-9}m[/tex]
Thus the longest wavelength of light that can be used to eject electrons from the surface of this metal via the photoelectric effect is 459 nm
