Dual nature of radiation and matter practice · Mixed difficulty

Option C is correct because increasing filament current increases intensity, and decreasing accelerating potential increases minimum wavelength.

Option A ($> v{\left( {\frac{4}{3}} \right)^{1/2}}$) is correct because the kinetic energy increases when the wavelength decreases, resulting in a higher speed.

Option A ($5: 1$) is correct because it is the ratio of the de-Broglie wavelengths of the particle and the photon, calculated using their energies and velocities.

Option A ($\frac{h}{p}$) is correct because the de-Broglie wavelength is inversely proportional to the momentum of the particle, as given by the formula $\lambda = \frac{h}{p}$.

Option A (I and II) is correct because photoelectric emission is not possible when the maximum kinetic energy is negative or when the threshold frequency is greater than the incident frequency.

Option C is correct because the de Broglie wavelength is inversely proportional to the square root of the mass, so the order is determined by the mass of the particles.

Option C (300) is correct because it is the approximate number of photons calculated using the given intensity, area, wavelength, and Planck's constant.

Option A ($6.63 \times 10^{-25} \mathrm{~kg} \mathrm{~ms}^{-1}; 1.24 \mathrm{~keV}; 1.51 \mathrm{~eV}$) is correct because it correctly calculates the momentum, photon energy, and electron kinetic energy using the given wavelength.

Option A is correct because the electronic charge is a fundamental constant and is independent of the gravitational acceleration.

The correct answer is B because both the assertion and the reason are correct, but the reason is not a correct explanation for the assertion. The assertion is true because emitted electrons have different kinetic energies, and the reason is true because different wavelengths have different energies, but this isn't the only reason for the assertion.

Option A ($2 / 3$) is correct because the de-Broglie wavelength is inversely proportional to the orbit number.

Option C is correct because both statements are true: de-Broglie wavelength is inversely proportional to the square root of temperature, and RMS velocity depends on temperature.

Option C (Both I & II are corect) is correct because photons with equal wavelengths have equal momentum, and photons with equal momentum have equal wavelengths, as defined by the relationship between momentum and wavelength.

Option B is correct because both the assertion and the reason are correct statements, but the reason does not explain the assertion.

Option A (2.15) is correct. The energy of a photon is calculated using the formula E = hf, where h is Planck's constant and f is the frequency.

Option C is correct because the speed of the electron in the electric field increases, decreasing its de Broglie wavelength, while the speed in the magnetic field remains constant.

Option A ($1.3 \times 10^{-27} \mathrm{~kg}-\mathrm{m} / \mathrm{sec}$) is correct because it is calculated using the formula $p = h/\lambda$.

Option B (Photoelectric effect) is correct because a photocell converts light energy into electrical energy based on the photoelectric effect.

Option C (Get deflected by electric and magnetic fields) is correct because deflection by electric and magnetic fields is a characteristic property of charged particles.

Option A (10 cm) is correct because the mean free path is longer than the tube length, so electrons don't collide within the tube, resulting in the Crookes dark space filling the entire tube.

Option A (Both Assertion and Reason are true, and Reason is the correct explanation for Assertion) is correct because increasing the power of a light source increases the number of photons emitted per second, and the energy of each photon remains constant.

Option A ($6.2 \mathrm~{KV}$) is correct because it is calculated using the formula relating minimum wavelength of X-rays to the operating voltage of the Coolidge tube.

Option C (Both the statements are correct) is correct because specific charge is the ratio of charge to mass, and mass increases with velocity, thus decreasing specific charge.

Option C ($36 \mathrm{~MPa}$) is correct because it is calculated using the bulk modulus formula and the volume expansion coefficient.

Option C ($hv - h{v_0}$) is correct because the maximum kinetic energy of emitted electrons is the difference between the photon energy and the work function.

Option A (2 eV) is correct because it is the kinetic energy calculated using Einstein's photoelectric equation with the given wavelength and work function.

Option D (Molybdenum) is the correct answer. Molybdenum has a relatively lower work function compared to the other given metals, making it easier to thermionically emit electrons at a lower temperature.

Option C (Both the statements are correct) is correct because photoelectrons are emitted almost instantaneously upon light incidence, and a photon transfers its energy to a single electron.

Option C (1 cm and ${10^{ - 3}}$ cm) is correct because air becomes conducting at low pressures, specifically within the range of 1 cm to ${10^{ - 3}}$ cm of Hg, due to increased mean free path and ionization.

The correct answer is B because both the assertion and the reason are correct, but the reason is not a correct explanation for the assertion. The spread in kinetic energies is due to varying depths of electron origin, not just the work function.