Given that
Wavelength of light \lambda = 488 nm = 488 * 10^{-9} m
Potential of photoelectrons V = 0.38 V
Work function of material = ?
Step 1: Get an expression for the work function
We know that
By conservation by law, Energy E = eV...........................(1)
Where, e - electric charge and V - potential of electrons
Einstein's photoelectric equation
Energy of proton E=h\upsilon\ -\ \phi
eV = h \frac{c}{\lambda} - \phi \because \text{ frequency } \upsilon = \frac{c}{\lambda}
Work function \phi = h \frac{c}{\lambda} - eV
Step 2: Plug in the know values in the above work function equation
Planck's constant h = 6.626*10^{-34} Js,
Speed of light c = 3*10^{8} m/s
Charge of electron e = 1.6*10^{-19} C
\phi = h \frac{c}{\lambda} - eV
\phi = \frac{6.626 * 10^{-34} * 3*10^{8}}{488 * 10^{-9}} - 1.6*10^{-19} * 0.38
\phi=\frac{\left(6.626*10^{-34}\right)\cdot\left(3\cdot10^8\right)}{\left(488*10^{-9}\right)\cdot\left(1.6\cdot\ 10^{-19}\right)}-\frac{\left(1.6*10^{-19}*0.38\right)}{1.6\cdot10^{-19}}
\phi=\frac{\left(4.0734*10^{-19}\right)}{1.6\cdot10^{-19}}-0.38
\phi = 2.5458 - 0.38
\phi = 2.1658 eV
Hence, work function of the material \phi = 2.1658 eV