PROBLEMS

A piece of wood was found to have ${}^{14}\mathrm{C}{/}^{12}\mathrm{C}$ ratio $0.7$ times that in a living plant. Calculate the period (in years) when the plant died.

$\left({\mathrm{t}}_{\frac{1}{2}} \text{for} {\mathrm{C}}^{14}=5760 \mathrm{yr}\right)$

$10.0$ gram-atom of an $\mathrm{\alpha }-$active radioisotope is disintegrating in a sealed container. In one hour, the $\mathrm{He}$ gas collected at $\mathrm{STP}$is $11.2$ litres. Calculate the half-life of the isotope supposing each nucleus yielding one $\mathrm{He}$ atom.

The disintegration rate for a sample containing ${}_{27}{}^{60}\mathrm{Co}$ as the only radioactive nuclide, is found to be $240$ atoms/minute. ${\mathrm{t}}_{\frac{1}{2}}$ of $\mathrm{Co}$ is $5.2$ years. Find the number of atoms of $\mathrm{Co}$ in the sample. How long(in years) must this radioactive sample be maintained before the rate falls to $100$ disintegration per minute?

A sample containing ${}_{88}{}^{234}\mathrm{Ra}$, which decays by $\mathrm{\alpha }$-particle emission, is observed to disintegrate at the following rate expressed as counts per minute $\left(\mathrm{cpm}\right)$. Calculate half-life (in days) of this nuclide. Give your answer up to two decimal places.

$\mathrm{t}=0,1000 \mathrm{cpm}$;

$\mathrm{t}=1 \mathrm{h}, 992 \mathrm{cpm}$;

$\mathrm{t}=10 \mathrm{h}, 924 \mathrm{cpm}$;

$\mathrm{t}=100 \mathrm{h}, 452 \mathrm{cpm}$;

$\mathrm{t}=250 \mathrm{h}, 138 \mathrm{cpm}$.

The thorium radioactive decay series produces one atom of ${}^{208}\mathrm{Pb}$ as the final disintegration product of an atom of ${}^{232}\mathrm{Th}$. ${\mathrm{t}}_{\frac{1}{2}}$ of ${}^{232}\mathrm{Th}$ is $1.39\times {10}^{10} \mathrm{years}$. A certain rock is found to have a mass ratio of ${}^{208}\mathrm{Pb}$ and ${}^{232}\mathrm{Th}$ as $14 : 1$. Determine the age of the rock in multiple of ${10}^{10}$ years.

The ratio of the number of atoms of two radioactive elements $\mathrm{A}$ and $\mathrm{B}$, in equilibrium with each other, is $3.1\times {10}^9:1$. If ${\mathrm{t}}_{\frac{1}{2}}$ of element $\mathrm{B}$ is $6.45$ years, calculate ${\mathrm{t}}_{1/2} (\mathrm{Half}-\mathrm{life})$ of element $\mathrm{A}$.

Give your answer up to one decimal place and if the answer is $\mathrm{X}\times {10}^{\mathrm{y}}, \text{give the value of X.}$

Which nucleus has higher binding energy per nucleon: ${}_{28}{}^{58}\mathrm{Ni} (57.941 \mathrm{amu})$ or ${}_{25}{}^{55}\mathrm{Mn} (54.939 \mathrm{amu})$? Mass of neutron is $1.00867 \mathrm{amu}$ and that of proton is $1.00728 \mathrm{amu}$.

For ${}_{92}{}^{238}\mathrm{U}$ the binding energy per nucleon is $7.576 \mathrm{MeV}$. What is the atomic weight of this isotope? 

Give your answer up to two places of decimal.