A graph of the variation with nucleon number \(A\) of the binding energy per nucleon is shown.
What is the approximate total energy, in MeV, needed to completely separate the nucleons of a \(^{180}_{72}\mathrm{Hf}\) nucleus?
Correct Answer: \( \boxed{\mathrm{C}} \)
The total binding energy of a nucleus is given by
\(\mathrm{binding\ energy}=(\mathrm{binding\ energy\ per\ nucleon})\times A\)
For \(A=180\), the graph gives a binding energy per nucleon of approximately \(8.0\,\mathrm{MeV}\).
Therefore,
\(E_{\mathrm{B}}\approx 8.0\times180\)
\(E_{\mathrm{B}}\approx1440\,\mathrm{MeV}\)
The energy required to completely separate the nucleons is equal to the total binding energy of the nucleus.
Hence, the correct answer is \( \boxed{\mathrm{C}} \).
Radioactive oxygen-15 \(\left(^{15}_{8}\mathrm{O}\right)\) decays according to the following equation:
\(^{15}_{8}\mathrm{O}\rightarrow X+\beta^{+}+\nu_{\mathrm{e}}\)
What are the proton number and the nucleon number of nuclide \(X\)?
| Proton number of \(X\) | Nucleon number of \(X\) | |
|---|---|---|
| (A) | \(7\) | \(14\) |
| (B) | \(9\) | \(14\) |
| (C) | \(7\) | \(15\) |
| (D) | \(9\) | \(15\) |
Correct Answer: \( \boxed{\mathrm{C}} \)
In beta-plus (\(\beta^+\)) decay, a proton in the nucleus changes into a neutron, producing a positron and an electron neutrino:
\(p\rightarrow n+\beta^{+}+\nu_{\mathrm{e}}\)
Therefore, the proton number decreases by \(1\), while the nucleon number remains unchanged.
For \(^{15}_{8}\mathrm{O}\):
\(\text{proton number of }X=8-1=7\)
\(\text{nucleon number of }X=15\)
Thus, \(X\) has proton number \(7\) and nucleon number \(15\).
Hence, the correct answer is \( \boxed{\mathrm{C}} \).
