$V = h(f - f_0)/e$; $f_3 = f_0$ (threshold)
$V_3 = h(f_0 - f_0)/e = 0$
$V_1 = h(f_1 - f_0)/e > 0$, $V_2 = h(f_2 - f_0)/e > 0$, $V_1 > V_2$ (since $f_1 > f_2$)
Answer: $V_1 > V_2$, $V_3 = 0$
Photoelectric effect: emission of electrons from metal surface when light of sufficient frequency is incident. Discovered by Hertz (1887), explained by Einstein (1905). Key observations: threshold frequency exists ($f_0$), instantaneous emission, $KE_{max}$ depends on $f$ not intensity, photocurrent proportional to intensity. Einstein\'s explanation: light comes in quanta (photons) each with energy $E = hf$. One photon ejects one electron if $hf > \phi$.
Photon: quantum of electromagnetic radiation. Energy: $E = hf = hc/\lambda$. Momentum: $p = E/c = h/\lambda = hf/c$. Mass: $m = 0$ (rest mass), but has relativistic mass $m = E/c^2$. Photon is its own antiparticle. Speed always $c$ in vacuum. Planck\'s constant: $h = 6.626\times10^{-34}$ J s. Compton effect: photon-electron collision, photon wavelength increases: $\Delta\lambda = (h/m_ec)(1-\cos\phi)$ (Compton wavelength shift).
de Broglie (1924): particles have wave nature. de Broglie wavelength: $\lambda = h/p = h/mv$. For electron accelerated through potential $V$: $\lambda = h/\sqrt{2meV}$. Davisson-Germer experiment (1927): confirmed electron diffraction, proving wave nature. Heisenberg uncertainty: $\Delta x \cdot \Delta p \geq h/4\pi$, $\Delta E \cdot \Delta t \geq h/4\pi$.
Bohr (1913): electrons move in circular orbits with quantised angular momentum $mvr = nh/2\pi$. Energy levels: $E_n = -13.6/n^2$ eV. Radius: $r_n = 0.529 n^2$ Angstrom. Transition: $hf = E_i - E_f$. Spectral series: Lyman (UV, $n_f=1$), Balmer (visible, $n_f=2$), Paschen (IR, $n_f=3$), Brackett ($n_f=4$), Pfund ($n_f=5$). Limitations: cannot explain multi-electron atoms, intensity of spectral lines, fine structure.