Examples with hints
| Examples with hints for lectures 1 to 3 |
| m1t1.1 Convert energy in MeV corresponding to a mass 1 atomic mass unit (amu). |
| Hint: First convert 1 amu to mass in kg. Use Einstien’s mass-energy relation E = mc2 to get the equivalent energy in Joule. Using conversion factor 1 MeV ~ 1.6 x 10 -13 Joule, you will get energy equivalent to mass 1 amu ~ 931 MeV. |
| m1t1.2 Calculate the mass of a 62Ni nucleus in kilograms . |
| Hint: Use the concept given in mt1.1. |
| m1t1.3 Use appropriate equations and plot the nucleon density distribution in case of Au nucleus. |
| Hint: The equations m1.1 and m1.2 are to be used. Calculate R for 197Au and use RAu in m1.1 and generate a plot between ρ (r) versus r. |
| m1t1.4 In order to calculate energy of a nucleon in a nucleus, one approach is to calculate the electrostatic energy required to insert a proton into the nucleus. Show that from this consideration the energy of a proton in a medium-weight (Z = 50, A = 120) nucleus turns out to be ~ 13 MeV. |
| Hint: Use the following relation to compute Coulomb’s energy |
/equ1.gif) |
| where, e = 1.6 X 10 -19 C ε 0 = 8.9 X 10 -12 C2 /N-m2 |
| m1t1.5 Consider a nucleus consisting of six protons, which are located in the following manner: two protons at z = /img1.gif) R on the body axis and four protons in the equatorial planes x = R and y = R. What is the quadrupole moment of the nucleus? |
| Hint: For a proton at a position z = r = R, x = y = 0, the value of Qd from equation m1.8 = eR2 . Now calculate for above geometry and you will find that net Qd of the nucleus is zero. |
| m1t1.6 Calculate gravitational and Coulomb interaction forces between two protons inside an nucleus and compare. |
| Hint: Use Newton’s law and Coulomb’s law to calculate the above. You will realize that how week gravitational force as compared to the other inside a nucleus. (from some particle physics/phenomenology course, calculate the same for strong interaction and compare the three. You will understand that the fundamental forces of nature are energetically so different, but still can be unfied). |