Question

If the energy of the incident radiation on a metal is increased by $10%$, the kinetic energy of the emitted photoelectrons increases from $0.5,eV$ to $0.75,eV$, then the work function of the metal is

• A. $2,eV$
• B. $1.5,eV$
• C. $1,eV$
• D. $2.5,eV$
• E. $1.8,eV$

Hint:

Physics Tip: Any increase in photon energy directly increases maximum kinetic energy by the same amount because work function remains constant.

Answer 1

The Correct Option is A

Concept:
Photoelectric equation: $$K_{\max}=E-\phi$$ where $E$ = photon energy, $\phi$ = work function.
Step 1: Form first equation.
Initial kinetic energy: $$E-\phi=0.5$$
Step 2: After 10% increase in energy.
New photon energy: $$1.1E$$ New kinetic energy: $$1.1E-\phi=0.75$$
Step 3: Subtract equations.
$$\left(1.1E-\phi\right)-\left(E-\phi\right)=0.75-0.5$$ $$0.1E=0.25$$ $$E=2.5,eV$$
Step 4: Find work function.
From first equation: $$2.5-\phi=0.5$$ $$\phi=2.0,eV$$
Hence correct option is (A). :contentReference[oaicite:1]{index=1}