A neutron with mass my moving with velocity vo collides elastically and head-on with a target particle with mass m₂ that is at rest. After the collision, the neutron moves with velocity vifand the target particle moves with velocity v2f- (a) Consider collisions of the neutron (mass = 1.0 atomic mass units (amu)) with the following stationary target particles 1. an electron (mass = 5.49 x 104 amu) 2. a proton (mass = 1.00 amu) 3. the nucleus of a bismuth atom (mass = 209 amu) 4. the nucleus of a nitrogen atom (mass = 14.0 amu) Match collisions 1-3 above with one of the following head-on collisions that we discussed in lecture: • the collision between two identical billiard balls, one of the billiard balls initially at rest the collision between a ping pong ball and a bowling ball, the ping pong ball initially a rest • the collision between a ping pong ball and a bowling ball, the bowling ball initially at rest (b) Calculate the ratio of the neutron's final kinetic energy to its initial kinetic energy (Ke/Ki)neutron for each of the collisions in (a). (answer: electron: K/K;=0.998: proton: K/K;=0; bismuth: K+/K; = 0.981; nitrogen: K+K;= 0.751) (c) What percentage of the neutron's initial kinetic energy is transferred to each target particle? Hint: Calculate (K) target (Ki)neutron (answer: electron: 0.22%; proton: 100%; bismuth: 1.9%; nitrogen: 25%) (d) Each of the answers to parts (b) and (c) should add up to 100%. Do they?

Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (ªHe) from gold-197 nuclei (197 Au). The energy of the incoming helium nucleus was 7.28 × 10-13 J, and the masses of the helium and gold nuclei were 6.68 × 10-27 kg and 3.29 × 10-25 kg, respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.) (a) If a helium nucleus scatters to an angle of 136° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus. 4He speed 197 Au velocity t 197 Au direction 14500000 0.0140 -17 m/s X m/s ° counterclockwise from the +x-axis (b) What is the final kinetic energy (in J) of the helium nucleus? 7.02e-13 J

Electron capture is a variant on beta-radiation.  The lightest nucleus to decay by electron capture is 7Be -- beryllium-7.  The daughter nucleus is 7Li -- lithium-7.  The electron is transformed into a massless particle (a neutrino): e − + 7 B e + ⟶ 7 L i + ν The initial electron is bound in the atom, so the beryllium mass includes the electron.  In fact, since the electron starts bound in the atom, a more-accurate statement of the nuclear reaction is probably: 7 B e ⟶ 7 L i + ν The masses are beryllium: 7.016929 u, and lithium: 7.016003 u, and refer to the neutral atom as a whole.  (Use uc and uc2 as your momentum and energy units -- but carry them along in your calculation.) The initial beryllium atom is stationary.  Calculate the speed of the final lithium nucleus in km/s. (all the energy released goes into the lighter particle.  c = 300,000 km/s)

Electron capture is a variant on beta-radiation.  The lightest nucleus to decay by electron capture is 7Be -- beryllium-7.  The daughter nucleus is 7Li -- lithium-7.  The electron is transformed into a massless particle (a neutrino): e − + 7 B e + ⟶ 7 L i + ν The initial electron is bound in the atom, so the beryllium mass includes the electron.  In fact, since the electron starts bound in the atom, a more-accurate statement of the nuclear reaction is probably: 7 B e ⟶ 7 L i + ν The masses are beryllium: 7.016929 u, and lithium: 7.016003 u, and refer to the neutral atom as a whole.  (Use uc and uc2 as your momentum and energy units -- but carry them along in your calculation.) The initial beryllium atom is stationary.  Calculate the speed of the final lithium nucleus in km/s. (You will make life much easier for yourself if you recognize that practically all the energy released goes into the lighter particle.  c = 300,000 km/s)