Rutherford fired a beam of alpha particles (helium nuclei) at a thin sheet of gold. An alpha particle was observed to be deflected by 90.0°; its speed was unchanged. The alpha particles used in the experiment had an initial speed of 2.4 ✕ 107 m/s and a mass of 6.7 ✕ 10−27 kg. Assume the alpha particle collided with a gold nucleus that was initially at rest. Find the speed of the nucleus after the collision.

3. A beam of helium-3 atoms (m = 3.016 u) is incident on a target of nitrogen-14 atoms (m = 14.003 u) at rest. Dur- ing the collision, a proton from the helium-3 nucleus passes to the nitrogen nucleus, so that following the col- lision there are two atoms: an atom of "heavy hydro- gen" (deuterium, m = 2.014 u) and an atom of oxygen-15 15.003 u). The incident helium atoms are moving at (m a velocity of 6.346 × 10° m/s. After the collision, the deu- terium atoms are observed to be moving forward (in the same direction as the initial helium atoms) with a velocity of 1.531 x 10' m/s. (a) What is the final velocity of the oxygen-15 atoms? (b) Compare the total kinetic energies before and after the collision.

Consider the following a-decay of the Uranium nucleus 236 U → 332Th + a. 90 (a) Show how the mass number (Aa) and atomic number (Za) of the alpha particle are obtained from this equation. (b) Calculate the Q-value (Qa) of the reaction. (c) Calculate the speed va = √2MQ of the alpha particle after it has been ejected from the parent nucleus, in terms of the speed of light c. M = -, mp and ma are the atomic masses (ma+mp) x ma mp of the daugher nucleus and the alpha particle, respectively. (d) Calculate the classical turning radius Re= 2Zpe²/Qa, where Zp is the atomic number of the daughter nucleus, and e² = 1.44 MeV. fm. (e) Calculate the decay probability Pa that the alpha particle will tunnel through the barrier. HINT: In calculating the probability, use the fact that ħc=197.327 MeV fm. The formula to use is given on page 5.

A beam of 6.76 MeV protons is incident on a target of 2713Al. Those that collide produce the following reaction. p + 2713Al  2714Si +1 + n (Neutral 2714Si has mass 26.986705 u.) Ignoring any recoil of the product nucleus, determine the kinetic energy of the emerging neutrons.  answer in MeV