Question

The work function of a metal is 2.5 × 10⁻¹⁹ J. (a) Find the threshold frequency for photoelectric emission. (b) If the metal is exposed to a light beam of frequency 6.0 × 10¹⁴ Hz, what will be the stopping potential?

Answer 1

Given:
Work function of a metal, W₀ = 2.5 × 10⁻¹⁹ J
Frequency of light beam, v = 6.0 × 10¹⁴ Hz

(a) Work function of a metal,
W₀ = hv₀,
where h = Planck's constant
v_{0 =} threshold frequency
$\therefore$ v₀ = $\frac{W_0}{h}$
$$\begin{gathered} \Rightarrow v_0=\frac{2.5\times {10}^{-19}}{6.63\times {10}^{-34}} \\ =3.77\times {10}^{14}\mathrm{Hz} \\ =3.8\times {10}^{14}\mathrm{Hz} \end{gathered}$$

(b) Einstein's photoelectric equation:
$e{V}_0=hv-W_0$,
where v = frequency of light
V_{0 =} Stopping potential
e = charge on electron
$$\begin{gathered} \therefore V_0=\frac{hv-{\mathrm{W}}_0}{e} \\ =\frac{6.63\times {10}^{-34}\times 6\times {10}^{14}-2.5\times {10}^{-19}}{1.6\times {10}^{-19}} \\ =\frac{3.97\times {10}^{-19}-2.5\times {10}^{-19}}{1.6\times {10}^{-19}}=0.91\mathrm{V} \end{gathered}$$