Quantum Mechanics Quiz: Trivia!

Explanation
The energy emitted by a black surface should not vary with time. This is because the emission of energy from a black surface is solely determined by its temperature and not by the duration for which it has been emitting energy. The energy emitted by a black surface is governed by the Stefan-Boltzmann law, which states that the total energy radiated is proportional to the fourth power of the temperature. Therefore, as long as the temperature remains constant, the energy emitted by the black surface will also remain constant over time.

Explanation
The emissive ability of a black body is given by the Stefan-Boltzmann Law, which states that the power emitted per unit area of a black body is proportional to the fourth power of its temperature. In this case, the sun emits maximum radiation at a wavelength of 0.52-micron meter. By using Wien's displacement law, we can determine the temperature of the sun's surface. Plugging this temperature into the Stefan-Boltzmann Law, we can calculate the emissive ability of the sun's surface, which is approximately 5.47 * 10^7 W/m2.

Explanation
Rayleigh-Jean's law holds good for longer wavelengths. This law describes the intensity of blackbody radiation as a function of wavelength and temperature. According to this law, the intensity of radiation increases with increasing wavelength. Therefore, it is valid for longer wavelengths, but not for shorter wavelengths.

Explanation
The Compton shift refers to the change in wavelength of X-rays or gamma rays when they are scattered by electrons. It is a phenomenon that occurs due to the interaction between photons and electrons. The incident radiation plays a crucial role in determining the magnitude of the Compton shift. As the energy of the incident radiation increases, the Compton shift also increases. Therefore, the correct answer is "Incident radiation."

Explanation
The zero-point energy for a particle in an infinite potential well is given by the equation E = (h^2)/(8mL^2), where h is Planck's constant, m is the mass of the particle, and L is the length of the well. In this case, we are given that the electron is confined to a 1 nm atom, so L = 1 nm = 1 x 10^-9 m. Plugging in the values, we can calculate the zero-point energy to be approximately 5.9 x 10^-29 J.

Explanation
According to the principles of quantum mechanics, the particle in a box refers to a hypothetical scenario where a particle is confined to a one-dimensional box. In this scenario, the particle is subject to the uncertainty principle, which means that it cannot have a definite position and momentum simultaneously. Therefore, the particle in a box can never be completely at rest, as it will always have some amount of motion or momentum. Hence, the statement "Particle in a box can never be at rest" is true.

Explanation
According to Heisenberg's uncertainty principle, it is impossible to simultaneously know the exact position and momentum of a particle. If the uncertainty in the position of an electron is zero, it means that its position is known with absolute certainty. However, this violates the uncertainty principle because if the position is known exactly, the uncertainty in momentum becomes infinite. Therefore, the uncertainty in momentum would be infinite if the uncertainty in the position of an electron is zero.

Explanation
The unit of Planck constant, denoted as h, is Joule x sec. This constant is used to relate the energy of a photon to its frequency. It is a fundamental constant in quantum mechanics and plays a crucial role in various equations and calculations in the field. The unit of Joule x sec represents the product of energy and time, which aligns with the nature of the Planck constant.