Quantum mechanics is one of the two revolutions in physics that took place in early Ith century. It simultaneously builds upon the principles discovered in classical mechanics [a.k.a. "Newtonian mechanics"] while upending classical mechanics by introducing new ideas and assumptions that cannot be derived from classical mechanics. Choose all statements below which correctly describe quantum mechanics, its assumptions, and;Ir or its consequences. Hint E] A new physical constant discovered by Max Planck plays an important role in every quantum mechanical phenomena. [J Quantum mechanics categorizes all physical things as particles or waves depending on whether the "thing'I obeys the quantization rule or not. C] Several physical quantities become quantizedallowed only in discrete quantitiesin some situations in quantum mechanics. DThe uncertainty principle says that no law of physics may be proven beyond a reasonable doubt. DThe rules of kinematicsparabolic trajectories, constantacceleration motions, etc.continue to be important in quantum mechanics. DThe ideas of energy and momentum continue to be important in quantum mechanical formulation of nature. The principle of relativity [also known as the First Postulate of Special Relativity] says that the laws of physics are the same in all inertial frames of reference. Choose all statements below which are correct according to the principle of relativity. ' Hint [:1 The kinetic energy of a 1k'ilogram mass is the same in all inertial reference frames. [3 The speed of a bird flying overhead is the same in all inertial reference frames. [:1 The natural oscillation frequency of a pendulum is the same in all inertial reference frames. D The net force on a mass accelerating at 1 mis2 is the same in all inertial reference frames. [:l The mass of a T-kilogram mass is the same in all inertial reference frames. Check your intuition and understanding of principle of relativity. a. Suppose that speed of sound in air under usual conditions [pressure of 1 atmosphere, room temperature, etc.) is 340 mr's. If you are in the pressurized cabin of an airplane flying at 250 mfs relative to the ground, wi'Ien you hear someone speak in the airplane, what is the speed of their sound? Hint for {a} Speed of sound made by someone on the airplane is mfs. b. Suppose that you are able to observe the sound waves while standing on the ground. I'n"|||"l'llat range of speeds of the sound waves in the airplane do you see, relative to you? Hint for is] , The speed of the sound wave propagating forward {to the front of the airplane} is mIs, and the speed of the sound wave propagating backward {to the back of the airplane} is mfs. Carbon-14, a naturally occurring unstable isotope of carbon, has a halflife of EEO years. Answer belowr questions. ' Hint a. in a sample of carbon containing 2 part per trillion of carbon14 [that is, 2 carbon14 atoms per every 1U\" atoms of carbon}, how much carbon-14 remains after 530 years? After 5130' yea rs, I part per trillion of carbon-14 remains in the sample. b. Carbon-14 is used for a technique called "carbon dating", which uses radioactive decay of carbon-14. if it can be determined that an artifact originally had 3.'l]l] X 1B\" carbon14 atoms originally but now only has 15m} x IDS carbon-14 atoms {carbon-14 haying decayed into other isotopes, such as nitrogen-14], how old do you estimate the artifact to be? ' Hint for {b} The artifact is estimated to be years old