Many heavy nuclei undergo spontaneous "alpha decay," in which the original nucleus emits an alpha particle (a helium nucleus containing two protons and two neutrons), leaving behind a "daughter" nucleus that has two fewer protons and two fewer neutrons than the original nucleus. Consider a radium-220 nucleus that is at rest before it decays to radon-216 by alpha decay. The mass of the radium-220 nucleus is 219.96274 u (unified atomic mass units) where 1 u = 1.6603 x 10-27 kg (approximately the mass of one nucleon). The mass of a radon-216 nucleus is 215.95308 u, and the mass of an alpha particle is 4.00151 u. Radium has 88 protons, radon has 86 protons, and an alpha particle has 2 protons. (Use 2.9979 x 108 m/s for the speed of light.)

Schrodinger's cat is one of the most common subjects in modern physics for cartoonists. Here's what Erwin Schrodinger said about his famous thought experiment, "One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following diabolical device (which must be secured against direct interference by the cat): In a Geiger counter, there is a tiny bit of radioactive substance, so small that perhaps in the course of one hour, one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges, and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if, meanwhile, no atom has decayed. The first atomic decay would have poisoned it. The function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal…

Consider the proton to be a spherical shell of charge of radius R. Using first order perturbation theory calculate the change in the binding energy of hydrogen due to the non-point-like nature of the proton. Does the sign of your answer make sense physically? Explain. Note: You may use the approximation R « ao throughout this problem, where ao is the Buhr radius.

Consider a proton confined within typical nuclear dimensions of 5×10^(−15) m. Estimate the minimum kinetic energy of the proton. Repeat this calculation for an electron confined within typical nuclear dimensions. Comment briefly on the physical significance of your results, given that the nuclear binding energy for a proton is typically in the range 1−10 MeV

A nucleus traveling at speed vnucleus = c(1 - 10-5) decays with the emission of a particle of speed vdecay particle = c(1 - 2 x 10-4) at an angle of 45°, as shown in the diagram above. i) What is the velocity (speed and direction) of the decay particle on transforming to the stationary frame of reference of the nucleus. Clearly explain the quantities used in your evaluation, and show the directions and signs of quantities. Give the speed of the decay particle in the form c(1 - ?). ii) If the decay particle was an electron, what was its total energy in the rest frame of the nucleus? What was its total energy in the original frame shown in the above diagram?Give your answers in units of MeV.