Class Tutorial 1 : 2NP Nuclear Physics
Dr W.N. Catford
1. Give the symbol for the following:
(a) the isotope of helium with mass number 4
(b) the isotope of tin with 66 neutrons
(c) an isotope with mass number 235 that contains 143 neutrons.
2. Given that the nuclear radius is proportional to A1/3 where A is the mass
number, and that the constant of proportionality is 1.2 fm then compute the
approximate radii of the nuclei of
(a) carbon with mass number A = 12,
(b) germanium with mass number A = 70,
(c) bismuth with mass number A = 209.
3. Given the above formula for the radius, and that the mass of a nucleon can
be estimated by the mass of a proton, 1.67 × 10−27 kg, calculate the density
of nuclei and hence the resultant mass if we could manufacture a nucleus with
radius 1 cm.
4. The binding energy of a nucleus is the amount by which its mass is reduced,
compared to the sums of the masses of all the nucleons inside it. If we write
this in terms of atomic masses, the electron masses (included in the atomic
masses) cancel out, so that in terms of atomic masses for an isotope with mass
number A of element X with Z protons and N neutrons, we can write
h
i
2
B = N mn + Zm(11 H) − m(A
Z XN ) c .
Use this formula to calculate the binding energy B and also the binding energy
238
per nucleon B/A for 56
26 F e30 and 92 U146 .
Atomic numbers: He Z = 2, Sn Z = 50, U Z = 92.
Atomic masses in atomic mass units (u): n has m = 1.008665, 11 H has m = 1.007825,
has m = 55.934942, 238
92 U has m = 238.050784.
56
26 Fe
Atomic mass unit: uc2 = 931.4943 MeV, u = 1.6605402 × 10−27 kg
W.N. Catford
Tutorial 1 / Spring Semester