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Carbon-14 is unstable and decays to a daughter nucleus along with an electron. T

ID: 977877 • Letter: C

Question

Carbon-14 is unstable and decays to a daughter nucleus along with an electron.  The Q-value for this decay is foundto be Q = 0.156476 MeV.d) [1 point] Find the atomic number, the mass number, and the chemical symbol for the daughter nucleus of thisdecay.

e) What is the mass of the daughter nucleus (in u)? [Hint: First find the mass of the Carbon-14 nucleus(the earlier number was the mass of the neutral Carbon-14 atom). Then use conservation of energy!]

f) What is the electron configuration of the ground-state carbon atom in spectroscopic notation?

g) Suppose one of the electrons were excited to a 4d state. What is the value of L, the magnitude of theangular momentum for this electron? What are the possible values of Lz, the z-component of angularmomentum? What are the possible values of the spin quantum number ms?

Explanation / Answer

1) 146C has the exact mass 14.003241

From the Q value we can find the difference

0.156476/931 = 1.681 x 10-4

Electron = 0.00054386734

M = Sum of the masses of products – Sum of the masses of reactants

If the reaction is exoergic i.e. Energy is released then the value of Q will be positive. On the other hand if the reaction is endoergic i.e. Energy is absorbed then the value of Q will be negative.

0.000168 = (0.00054386+ x) - 14.003241

x = 14.002865

So the possible daughter nucleus is

2) electron configuration of the ground-state carbon atom in spectroscopic notation 1s22s22p2- 3P2