(a) Energy is required to separate a nucleus into its constituent nucleons, as t
ID: 1410968 • Letter: #
Question
(a) Energy is required to separate a nucleus into its constituent nucleons, as the drawing indicates; this energy is the total binding energy of the nucleus. In a similar way one can speak of the energy that binds a single nucleon to the remainder of the nucleus. For example, separating nitrogen 7N15 into 7N14 and a neutron takes energy equal to the binding energy of the neutron. Find the energy (in MeV) that binds the neutron to the 7N15 nucleus by considering the mass of 7N14 (atomic mass = 14.003074 u) and the mass of 0n1 (atomic mass = 1.008665 u), as compared to the mass of 7N15 (atomic mass = 15.000108 u). (b) Similarly, one can speak of the energy that binds a single proton to the 7N15 nucleus. Following the procedure outlined in part (a), determine the energy (in MeV) that binds the proton (atomic mass = 1.007825 u) to the 7N15 nucleus. (c) Which nucleon is more tightly bound, the neutron or the proton?
Explanation / Answer
Binding energies are usually expressed in MeV, but mass defect is usually expressed in amu. T o convert from one to the other multiply by 931.5016 MeV/amu
a) 931.5016 MeV/amu x (15.000108 - (14.003074 + 1.008665)) = -10.76MeV which is nearly equal to -10.8MeV
- symbol means it binds the neutron
b) 931.5016 MeV/amu x (15.000108 - (14.003242 + 1.007825))
= -10.1456MeV which is nearly equal to -10.2 MeV
- symbol means it binds the electrons
c) since -10.76 MeV is more negative than -10.14 MeV the neutron is more tightly bound
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