Problems

The half-life of a radioactive isotope is $120 \mathrm{d}$. How many days would it take for the decay rate of a sample of this isotope to fall to one-fourth of its initial value?

What is the nuclear mass density ${\rho }_{\mathrm{m}}$ of (a) the fairly low-mass nuclide ${}^{55}\mathrm{Mn}$ and (b) the fairly high-mass nuclide $20\% \mathrm{Bi}$? (c) Compare the two answers with an explanation. What is the nuclear charge density ${\rho }_{\mathrm{q}}$ of (d) ${}^{55}\mathrm{Mn}$ and (e) ${}^{209}\mathrm{Bi}$? (f) Compare the two answers, with an explanation.

In a Rutherford scattering experiment, assume that an incident alpha particle (radius $1.80 \mathrm{fm}$) is headed directly towards a target Gold nucleus (radius $6.23 \mathrm{fm}$). What energy must the alpha particle have to just barely touch the Gold nucleus?

Because the neutron has no charge, its mass must be found in some way other than by using a mass spectrometer. When a neutron and a proton meet (assume both to be almost stationary), they combine and form a deuteron emitting a gamma ray whose energy is $2.2233 \mathrm{MeV}$. The masses of the proton and the deuteron are $1.007276467 \mathrm{u}$ and $2.013553212 \mathrm{u}$, respectively. Find the mass of the neutron from these data.

A dose of $8.20 \mathrm{\mu Ci}$ of a radioactive isotope is injected into a patient. The isotope has a half-life of $3.0 \mathrm{h}$. How many of the isotope parents are injected? $\left(1 \mathrm{Ci}=3.7\times {10}^{10} {\mathrm{s}}^{-1}\right)$

A $10.2 \mathrm{MeV}$ $\mathrm{Li}$ nucleus is shot directly at the centre of a $\mathrm{Ds}$ nucleus. At what centre-to-centre distance does the $\mathrm{Li}$ momentarily stop assuming that $\mathrm{Ds}$ does not move?

What is the binding energy per nucleon of ${}^{262}\mathrm{Bh}$? The mass of the atom is $262.1231 \mathrm{u}$.

$m_{\mathrm{p}}=1.007825 \mathrm{u}$, $m_{\mathrm{n}}=1.008665 \mathrm{u}$, $m_{\mathrm{Bh}}=262.1231\mathrm{u}$.

The nuclide ${}^{14}\mathrm{C}$ contains (a) how many protons and (b) how many neutrons?