4. Calculate the magnetic moment of the following...

4. Calculate the magnetic moment of the following nucleus:- S(16,33), Cu(29,63), Bi(83,209) and Mg(12,25) 5. Estimate the quadrupole moment of the ground state of the following nuclei- F(9,17), Cu(29,63), Ni(28,61) and K(19,41) (Note: consider the uniform charge distribution of the nucleus)

4.6 A nucleus with quadrupole moment Q finds itself in a cylindrically symmetric electric field with a gradient (∂E_z/∂z)_0 along the z axis at the position of the nucleus. (a) Show that the energy of quadrupole interaction is W = - e/4 Q (∂E_z/∂z)_0 (b) If it is known that Q = 2 x 10^-28 m^2 and that W/h is 10 MHz, where h is Planck's constant, calculate (∂E_z/∂z)_0 in units of e/4πε_0a_0^3, where a_0 = 4πε_0ℏ^2/me^2 = 0.529 x 10^-10 m is the Bohr radius in hydrogen. (c) Nuclear charge distributions can be approximated by a constant charge density throughout a spheroidal volume of semimajor axis a and semiminor axis b. Calculate the quadrupole moment of such a nucleus, assuming that the total charge is Ze. Given that Eu^153 (Z = 63) has a quadrupole moment Q = 2.5 x 10^-28 m^2 and a mean radius R = (a + b)/2 = 7 x 10^-15 m determine the fractional difference in radius (a - b)/R.

Adi S.

Question

4. Calculate the magnetic moment of the following nucleus:- S(16,33), Cu(29,63), Bi(83,209) and Mg(12,25) 5. Estimate the quadrupole moment of the ground state of the following nuclei- F(9,17), Cu(29,63), Ni(28,61) and K(19,41) (Note: consider the uniform charge distribution of the nucleus)

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