Dual Nature of Radiation and Matter: NEET previous year questions

$E = h\nu$ gives the energy of a photon (IV); diffraction and interference demonstrate the wave nature of light (III); $\lambda = h/p$ is the de Broglie wavelength of a particle (I); and the Compton effect confirms the particle nature of light (II). Hence P-IV, Q-III, R-I, S-II, which is option (4).

Photoemission requires photon energy $\dfrac{hc}{\lambda} \geq W_0$, i.e. wavelength $\lambda \leq \dfrac{hc}{W_0}$. Here $\dfrac{hc}{W_0} = \dfrac{6.6\times10^{-34}\times3\times10^{8}}{6.6\times1.6\times10^{-19}} \approx 187.5\ \text{nm}$. Any wavelength longer than this cannot eject electrons; $200\ \text{nm} > 187.5\ \text{nm}$, so it produces no photoelectric effect.

Photocurrent is set by the NUMBER of photons striking the surface per second, so it is proportional to the source power and falls linearly with $t$. Stopping potential, by contrast, depends only on the maximum kinetic energy of the emitted electrons, $eV_0 = h\nu - \phi_0$, which is fixed by the FREQUENCY and the work function - neither of which changes here. So $|V|$ stays flat while $I$ decays. NCERT Class 12, Dual Nature of Radiation and Matter.

Why the other options are wrong:

- (2) treats stopping potential as intensity-dependent, the single most common photoelectric misconception
- (3) swaps the roles entirely, tying current to frequency and stopping potential to intensity
- (4) assumes neither quantity responds to the source, ignoring that current tracks photon flux

Emission occurs only when the incident wavelength is SHORTER than the threshold wavelength. Cell 1 has $\lambda_1 < \lambda$, so the photons are too weak and $V_1 = 0$. For the other two, $eV_0 = hc\left(\frac{1}{\lambda} - \frac{1}{\lambda_{th}}\right)$; a LARGER threshold wavelength means a smaller work function and hence a larger stopping potential. Since $\lambda_3 \gg \lambda_2$, the term $1/\lambda_3$ is nearly zero and $V_3 > V_2$. NCERT Class 12, Dual Nature of Radiation and Matter (Einstein's photoelectric equation).

A photon's momentum is $p = \frac{E}{c} = \frac{20 \times 1.6 \times 10^{-19}}{3 \times 10^8} \approx 1.07 \times 10^{-26}\ \text{kg m s}^{-1}$. A non-relativistic electron of the same kinetic energy has $p = \sqrt{2mE} = \sqrt{2(9 \times 10^{-31})(3.2 \times 10^{-18})} = 2.4 \times 10^{-24}\ \text{kg m s}^{-1}$. The ratio is therefore about 225 - a massive particle carries far more momentum than a photon of the same energy, because $p \propto \sqrt{E}$ for matter but $p \propto E$ for light. NCERT Class 12, Dual Nature of Radiation and Matter.

For an electron, $\lambda$(nm) = 1.227/$\sqrt{V}$. Setting $\lambda = 1.227 \times 10^{-2}$ nm gives $\sqrt{V}$ = 100 and V = 10$^{4}$ V. Chapter: Dual Nature of Radiation and Matter.

The new frequency is 0.75ν$_{0}$, below the threshold ν$_{0}$. No electrons are emitted irrespective of the doubled intensity, so the photoelectric current is zero. Chapter: Dual Nature of Radiation and Matter.