A light from Paschen series of hydrogen atom is able to eject photoelectrons from a metal. Then the work function of the metal is:
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For any hydrogen spectral series ending at level \(n_f\), the maximum photon energy is obtained at the series limit:
\[
E_{\max}=\frac{13.6}{n_f^2}\,\text{eV}
\]
For the Paschen series, \(n_f=3\), giving
\[
E_{\max}\approx 1.51\,\text{eV}.
\]
Step 1: Find the maximum photon energy in the Paschen series. Paschen series: transitions end at \( n = 3 \). The series limit (\( n = \infty \to 3 \)) gives the maximum photon energy: \[ E_{max} = 13.6\times\frac{1}{3^2} = \frac{13.6}{9} \approx 1.51\,\text{eV} \]
Step 2: Apply the photoelectric threshold condition. Photoelectrons are ejected only if photon energy exceeds the work function. The maximum Paschen photon (1.51 eV) can eject electrons from a metal with work function up to about 1.51 eV. The closest answer among the options is \[ \boxed{1.54\,\text{eV}} \]