Respuesta :
Answer: The wavelength of light required is [tex]5.43\times 10^{-7}m[/tex]
Explanation:
To calculate the threshold wavelength for a given work function, we use the equation:
[tex]\phi =h\nu_o[/tex]
where,
[tex]\phi[/tex] = work function of the potassium metal = [tex]2.29eV=3.66\times 10^{-19}J[/tex] (Conversion factor: [tex]1eV=1.6\times 10^{-19}[/tex] )
h = Planck's constant = [tex]6.626\times 10^{-34}Js[/tex]
[tex]\nu_o=\frac{c}{\lambda _o}[/tex]
c = speed of light = [tex]3\times 10^9m/s[/tex]
[tex]\lambda_o[/tex] = wavelength of light
Putting values in above equation:
[tex]3.66\times 10^{-19}J=\frac{6.626\times 10^{-34}Js\times 3\times 10^8m/s}{\lambda_o}\\\\\lambda_o=\frac{6.626\times 10^{-34}Js\times 3\times 10^8m/s}{3.66\times 10^{-19}J}=5.43\times 10^{-7}m[/tex]
Hence, the wavelength of light required is [tex]5.43\times 10^{-7}m[/tex]
