+2 Physics Unit 7 - Dual Nature Of Radiation And Matter And Relativity

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The de Broglie wavelength of a moving particle is given by λ = h/p, where h is the Planck's constant and p is the momentum of the particle. The kinetic energy of a particle can be related to its momentum by the equation E = p^2/2m, where m is the mass of the particle. Therefore, we can rewrite the de Broglie wavelength equation as λ = h/√(2mE). Since the kinetic energy of the particle is given as E, the correct answer is (1) as it represents the correct equation for the de Broglie wavelength.

The photoelectric effect refers to the phenomenon where electrons are emitted from a material when it is exposed to light. The correct answer is "quantum theory of light" because this theory explains that light is composed of discrete packets of energy called photons. According to the quantum theory of light, when photons strike the surface of a material, they transfer their energy to electrons, causing them to be ejected from the material. This theory successfully explains the observed behavior of the photoelectric effect, including the dependence on the frequency of light and the existence of a threshold frequency.

At the threshold frequency, the velocity of the electrons is zero because the threshold frequency is the minimum frequency of light required to eject electrons from a metal surface in the photoelectric effect. At this frequency, the energy of the photons is just enough to overcome the binding energy of the electrons, causing them to be released from the surface. Since the electrons are being released from rest, their initial velocity is zero.

The stopping potential of a metal surface is independent of the intensity of incident radiation because the stopping potential is determined by the energy of the incident photons, which is related to the frequency of the radiation. The intensity of the radiation only affects the number of photons incident on the surface, not their individual energy. Therefore, changing the intensity of the radiation will not change the stopping potential.

The wavelength of a matter wave, also known as de Broglie wavelength, is determined by the momentum of the particle. It is given by the equation λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum. The charge of the particle does not affect its momentum, so it is independent of the wavelength.

According to the theory of relativity, the length of a rod in motion appears to be shorter than its rest length when observed from a stationary frame of reference. This phenomenon is known as length contraction. As an object moves faster, its length in the direction of motion appears to decrease. Therefore, the correct answer is "is less than its rest length."

The threshold frequency of a photoelectric material is the minimum frequency of light required to eject electrons from the material's surface. The energy of a photon is given by E = hf, where h is Planck's constant and f is the frequency of light. The work function, which is the minimum energy required to eject an electron, is given by W = hf0, where f0 is the threshold frequency. Since the work function is 3.3 eV, we can equate the two equations to find f0 = W/h = 3.3 eV / h. Therefore, the threshold frequency is equal to 3.3 eV / h.

If 1 kg of a substance is fully converted into energy, the energy produced would be a significant amount. The conversion of mass into energy is described by Einstein's famous equation, E=mc², where E represents energy, m represents mass, and c represents the speed of light. According to this equation, a small amount of mass can produce a large amount of energy. Therefore, the correct answer is (1), indicating that a substantial amount of energy would be produced if 1 kg of a substance is fully converted.

The momentum of an electron is inversely proportional to its wavelength according to the de Broglie equation. Since the given electron has a shorter wavelength of 2 Å, it means that its momentum will be larger compared to an electron with a longer wavelength. Therefore, the correct answer is (3).