Question

(i) The semi-empirical mass formula (SEMF) may be written in the form m(Z,A) = Zm_p+(A-Z)m_n-a_vA+a_sA^{2/3}+a_C frac{Z^2}{A^{1/3}}+a_A frac{(A-2Z)^2}{A}+frac{a_p}{A^{1/2}}?; ? = egin{pmatrix} +1 & O-O \ 0 & E-O \ -1 & E-E end{pmatrix}, where m_p is the mass of the proton and m_n the mass of the neutron. The five coefficients in the SEMF take on the following values in MeV: a_v = 15.8, a_s = 17.8, a_C = 0.71, a_A = 23.7, a_p = 11.2. (a) The nucleus ^{235}_{92}U can undergo spontaneous fission. One of the many fission channels is ^{235}_{92}U ? ^{87}_{35}Br + ^{145}_{57}La + 3 n. Estimate the energy released in this channel. (b) What will happen to the ^{87}_{35}Br and ^{145}_{57}La nuclei? (ii) Figure 2 at the end of the paper shows a schematic diagram of the nuclear energy levels. The nuclear magnetic dipole moment is given by ?_J = g_J?_NJ. The g_J factor depends on the spin and orbital angular momentum of the contributing nucleons. For even-odd nuclei there is a special case J = j = l ± 1/2 such that: j = l + frac{1}{2} : g_J = g_j = left(1 - frac{1}{2j} ight)g_l + left(frac{1}{2j} ight)g_s, j = l - frac{1}{2} : g_J = g_j = frac{1}{(j+1)} left[(j+frac{3}{2})g_l - frac{1}{2}g_s ight], where g_s = 5.6, -3.8 for the proton, neutron respectively. (a) Use the shell model to predict the spin-parity J^P and the nuclear magnetic moment ?_J (in units of the nuclear magneton ?_N) of the ground-state nuclei ^{12}_6C, ^{31}_{15}P. (b) The experimentally measured magnetic moment for ^{31}_{15}P is 1.13?_N. Explain why the value you have calculated agrees or disagrees with this.

          (i) The semi-empirical mass formula (SEMF) may be written in the form

m(Z,A) = Zm_p+(A-Z)m_n-a_vA+a_sA^{2/3}+a_C frac{Z^2}{A^{1/3}}+a_A frac{(A-2Z)^2}{A}+frac{a_p}{A^{1/2}}?; ? = egin{pmatrix} +1 & O-O \ 0 & E-O \ -1 & E-E end{pmatrix},

where m_p is the mass of the proton and m_n the mass of the neutron. The five coefficients in the SEMF take on the following values in MeV: a_v = 15.8, a_s = 17.8, a_C = 0.71, a_A = 23.7, a_p = 11.2.

(a) The nucleus ^{235}_{92}U can undergo spontaneous fission. One of the many fission channels is

^{235}_{92}U ? ^{87}_{35}Br + ^{145}_{57}La + 3 n.

Estimate the energy released in this channel.
(b) What will happen to the ^{87}_{35}Br and ^{145}_{57}La nuclei?

(ii) Figure 2 at the end of the paper shows a schematic diagram of the nuclear energy levels.
The nuclear magnetic dipole moment is given by ?_J = g_J?_NJ. The g_J factor depends on the spin and orbital angular momentum of the contributing nucleons. For even-odd nuclei there is a special case J = j = l ± 1/2 such that:

j = l + frac{1}{2} : g_J = g_j = left(1 - frac{1}{2j}
ight)g_l + left(frac{1}{2j}
ight)g_s,
j = l - frac{1}{2} : g_J = g_j = frac{1}{(j+1)} left[(j+frac{3}{2})g_l - frac{1}{2}g_s
ight],

where g_s = 5.6, -3.8 for the proton, neutron respectively.
(a) Use the shell model to predict the spin-parity J^P and the nuclear magnetic moment ?_J (in units of the nuclear magneton ?_N) of the ground-state nuclei
^{12}_6C, ^{31}_{15}P.

(b) The experimentally measured magnetic moment for ^{31}_{15}P is 1.13?_N. Explain why the value you have calculated agrees or disagrees with this.

$(i) The semi-empirical mass formula (SEMF) may be written in the form m(Z,A) = Zmp+(A-Z)mn-avA+asA^2/3+aC fracZ^2A^1/3+aA frac(A-2Z)^2A+fracapA^1/2?; ? = eginpmatrix +1 O-O 0 E-O -1 E-E endpmatrix, where mp is the mass of the proton and mn the mass of the neutron. The five coefficients in the SEMF take on the following values in MeV: av = 15.8, as = 17.8, aC = 0.71, aA = 23.7, ap = 11.2. (a) The nucleus ^23592U can undergo spontaneous fission. One of the many fission channels is ^23592U ? ^8735Br + ^14557La + 3 n. Estimate the energy released in this channel. (b) What will happen to the ^8735Br and ^14557La nuclei? (ii) Figure 2 at the end of the paper shows a schematic diagram of the nuclear energy levels. The nuclear magnetic dipole moment is given by ?J = gJ?NJ. The gJ factor depends on the spin and orbital angular momentum of the contributing nucleons. For even-odd nuclei there is a special case J = j = l ± 1/2 such that: j = l + frac12 : gJ = gj = left(1 - frac12j ight)gl + left(frac12j ight)gs, j = l - frac12 : gJ = gj = frac1(j+1) left[(j+frac32)gl - frac12gs ight], where gs = 5.6, -3.8 for the proton, neutron respectively. (a) Use the shell model to predict the spin-parity J^P and the nuclear magnetic moment ?J (in units of the nuclear magneton ?N) of the ground-state nuclei ^126C, ^3115P. (b) The experimentally measured magnetic moment for ^3115P is 1.13?N. Explain why the value you have calculated agrees or disagrees with this.$

Added by Stacy M.

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