NEET Uncategorized MCQs & PYQs

Maximum kinetic energy is given by $K = E - W$. For the first radiation, $K_1 = 1.0 - 0.5 = 0.5 eV$. For the second radiation, $K_2 = 2.5 - 0.5 = 2.0 eV$. The ratio of their kinetic energies is $K_1/K_2 = 0.5/2.0 = 1/4$. Since $K \propto v^2$, the ratio of speeds is $v_1/v_2 = \sqrt{K_1/K_2} = \sqrt{1/4} = 1/2$.

Useful power for light emission is $P = 25\% \text{ of } 200 W = 50 W$. The energy of one photon is $E = \frac{hc}{\lambda} = \frac{6.6 \times 10^{-34} \times 3 \times 10^8}{0.6 \times 10^{-6}} = 3.3 \times 10^{-19} J$. The number of photons emitted per second is $n = \frac{P}{E} = \frac{50}{3.3 \times 10^{-19}} \approx 1.5 \times 10^{20}$.

The intensity of light $I$ is inversely proportional to the square of the distance $r$ from a point source, so $I \propto \frac{1}{r^2}$ . When the distance is doubled from $0.5 m$ to $1.0 m$ , the intensity becomes $\frac{1}{4}$ of its initial value. Since the number of photoelectrons liberated is directly proportional to intensity, it will also be reduced by a factor of 4.

From Einstein's photoelectric equation, the initial maximum kinetic energy is $K = h\nu - E_0$ . When the frequency is doubled, the new incident energy is $2h\nu$ . The new maximum kinetic energy is $K' = 2h\nu - E_0$ . This can be rewritten as $K' = h\nu + (h\nu - E_0) = h\nu + K$ .

Initially, $\frac{1}{2}mv_1^2 = E_1 - W = 2h\nu_0 - h\nu_0 = h\nu_0$ . Finally, $\frac{1}{2}mv_2^2 = E_2 - W = 5h\nu_0 - h\nu_0 = 4h\nu_0$ . Taking the ratio gives $(\frac{v_2}{v_1})^2 = 4$ , so $v_2 = 2v_1$ . Substituting the given velocity, $v_2 = 2 \times (4 \times 10^6) = 8 \times 10^6 m/s$ .

Cathode rays are streams of fast-moving electrons, which are negatively charged particles. Because they carry an electric charge, they are readily deflected by both electric and magnetic fields. Therefore, the statement that they do not deflect in an electric field is incorrect.

Phenomena such as interference, diffraction, and polarization are successfully explained by the wave theory of light. The photoelectric effect, however, can only be explained by assuming that light consists of discrete energy packets or particles called photons, demonstrating its particle nature.

The intensity of incident light $I$ varies with distance as $I \propto \frac{1}{d^2}$ . When the distance is halved to $d/2$ , the intensity becomes $\frac{1}{(1/2)^2} = 4$ times its original value. Since the number of photoelectrons emitted per second is directly proportional to intensity, it also becomes four times.

Albert Einstein used Max Planck's quantum hypothesis to successfully explain the photoelectric effect. He proved that light interacts with matter as discrete quanta of energy (photons), where the energy of each photon is given by $E = h\nu$ .

J.J. Thomson discovered the electron and determined its specific charge (the charge-to-mass ratio, $e/m$ ). Once Robert Millikan independently measured the fundamental charge ( $e$ ), Thomson's ratio allowed for the indirect evaluation of the electron's mass.