Some Nuclear Properties — Question 1

Question 1

Isotope bookkeeping separates nuclear composition from ionic charge

A nucleus is written ${}^{64}_{29}X$. Its ion carries net charge $+2e$. A second isotope has the same proton number but three additional neutrons.

1. Find the numbers of protons, neutrons and bound electrons in the first ion.

2. Write the second isotope in nuclear notation and find the fractional change in nucleon count.

Question 1 - Solution

Isotope bookkeeping separates nuclear composition from ionic charge

(a) Method and calculation

$$\boxed{Z=29,\quad N=A-Z=64-29=35}.$$$$Q/e=Z-N_e=2\Rightarrow\boxed{N_e=27}.$$

(b) Interpretation and further calculation

$$N\prime=38,\quad A\prime=29+38=67\Rightarrow\boxed{{}^{67}_{29}X}.$$$$\boxed{(A\prime-A)/A=3/64=.046875=4.69\%}.$$

Physical check

Ionization changes the electron count but neither Z nor A. Isotopes share a proton number while differing in neutron number.