Correct answer: 1.6 × 10^15 Hz
The energy of the photon emitted during the transition from the first excited state to the ground state in hydrogen is 10.2 eV. Using the photoelectric equation, the threshold frequency is calculated as \( f_0 = \frac{E - eV_0}{h} \), where \( E = 10.2 \) eV, \( eV_0 = 3.57 \) eV, and \( h = 4.14 \times 10^{-15} \) eV·s. Solving gives \( f_0 = 1.6 \times 10^{15} \) Hz.