no idea please help i need the full solution Write down the

no idea, please help! i need the full solution!

Write down the decay process for B^12_5. calculate the change in energy for the reaction? show the shell model for the reaction and explain how this shows which element is stable? calculate the binding energies and the binding energy per nucleon for the reaction. does this also enable you to tell which should be stable by calculating the binding energy and binding energy per nucleon for a stable form of boron.

Solution

a) ¹²B₅ = ¹²C₆ + e^- + (anti-neutrino)

b) Change in energy for the reaction Q = [m(¹²B₅) – m(¹²C₆)]c²

So, Q = (12.014352 – 12)×931.5 MeV = 13.37 MeV

c) 12B₅ has 5 proton and 7 neutron.

5 proton 1s_1/2 1p_3/2 (incomplete shell)

7 neutron 1s­_1/2 1p_3/2 1p_1/2 (incomplete shell)

C₆ has 6 proton and 6 neutron,

6 proton 1s_1/2 1p_3/2 (complete shell)

6 neutron 1s_1/2 1p_3/2 (complete shell)

Complete shells are stable in shell model. So, ¹²C₆ is the stable element.

d) Binding energy E_B = Zm_pc² +Nm_nc² – m_Ac² + Zm_ec²

Z = number of proton, N = number of neutron

So, the binding energy of ¹²B₅

= (5×938.28) + (7×939.57) - (12.014352×931.5) + (5×0.51) = 79.57 MeV

Binding energy per nucleon = E_B/A = 79.57/12 = 6.63 MeV

And the binding energy of ¹²C_6­

= (6×938.28) + (6×939.57) - (12×931.5) + (6×0.51) = 91.98 MeV

Binding energy per nucleon = E_B/A = 91.98/12 = 7.66 MeV

e) Binding energy per nucleon of ¹²C_6­ is larger than ¹²B₅ . So, ¹²C_6­ is the stable element.