Answer:
A. [tex]\lambda_0=550\ nm[/tex]
Explanation:
The work function of the potassium = [tex]3.68\times 10^{-19}\ J[/tex]
For maximum wavelength, the light must have energy equal to the work function. So,
[tex]\psi _0=\frac {h\times c}{\lambda_0}[/tex]
Where,
h is Plank's constant having value [tex]6.626\times 10^{-34}\ Js[/tex]
c is the speed of light having value [tex]3\times 10^8\ m/s[/tex]
[tex]\lambda_0[/tex] is the wavelength of the light being bombarded
[tex]\psi _0=Work\ function[/tex]
Thus,
[tex]3.68\times 10^{-19}=\frac {6.626\times 10^{-34}\times 3\times 10^8}{\lambda_0}[/tex]
[tex]\frac{3.68}{10^{19}}=\frac{19.878}{10^{26}\lambda_0}[/tex]
[tex]3.68\times \:10^{26}\lambda_0=1.9878\times 10^{20}[/tex]
[tex]\lambda_0=5.50\times 10^{-7}\ m[/tex]
Also,
1 m = 10⁻⁹ nm
So,
[tex]\lambda_0=550\ nm[/tex]
