Many radioactive sources emit neutrons. One way of detecting them is by measuring the light (energy) given off when they are captured by protons (for example, when they enter water, which contains many hydrogen atoms, each one of which has a proton for its nucleus). The released energy from one such capture is 2.22 MeV in the form of high-energy light (a gamma ray; see Section 20.5). The combined neutron and proton is stable and called a deuteron.
(a) Avery slow neutron (i. e., neglect its kinetic energy) is captured by a proton. How should the resulting deuteron’s mass compare to the sum of the neutron and proton masses (1) md = mp + mn, (2) md > mp + mn, or (3) md < mp + mn?
(b) The proton and neutron masses are mp = 1.672 92 x 10-27 kg and mn = 1.674 93 x 10-27 kg. Determine the mass (in kilograms) of the deuteron (also to six significant figures).
(c) If the gamma ray goes on, it can eventually annihilate and create an electron– positron pair (the positron is the antiparticle of the electron— identical except for a positive charge +e). How much kinetic energy will the electron and positron together have?