Answer:
The longest wavelength equals [tex]0.4\times 10^{-6}m[/tex]
Explanation:
According to Einstein's photoelectric equation we have
[tex]E_{incident}\geq \phi [/tex]
where
[tex]E_{incident}[/tex] is the energy of the incident light
[tex]\phi [/tex] is the work function of the metal
The incident energy of the light with wavelength [tex]\lambda [/tex] is given by
[tex]E_{incident}=h\cdot \frac{c}{\lambda}[/tex]
Thus the photoelectric equation reduces to
[tex]h\cdot \frac{c}{\lambda}\geq \phi\\\\h\cdot c\geq \lambda \times \phi\\\\\therefore \lambda\leq \frac{h\cdot c}{\phi}[/tex]
Thus applying values we get
[tex]\lambda\leq \frac{6.62\times 10^{-34}\times 3\times 10^{8}}{3.10\times 1.602\times 10^{-19}}\\\\\therefore \lambda\leq 0.4\times 10^{-6}m[/tex]
Hence The longest wavelength equals [tex]0.4\times 10^{-6}m[/tex]
