When the energy of incident radiation is increased by \( 50\% \), the maximum kinetic energy of photoelectrons from a metal surface increases from \( 1\ \mathrm{eV} \) to \( 2.5\ \mathrm{eV} \). The work function of the metal is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 2\ \mathrm{eV} \)
By Einstein’s photoelectric equation, the maximum kinetic energy is the photon energy minus the work function:
\( K_{\max} = E - \phi_{0} \)
Before and after the 50% increase:
\( 1\,\mathrm{eV} = E - \phi_{0} \quad (1) \)
\( 2.5\,\mathrm{eV} = 1.5E - \phi_{0} \quad (2) \)
Subtracting (1) from (2):
\( 1.5\,\mathrm{eV} = 0.5E \ \Rightarrow\ E = 3\,\mathrm{eV} \)
\( \phi_{0} = E - K_{\max} = 3\,\mathrm{eV} - 1\,\mathrm{eV} = 2\,\mathrm{eV} \)