David Sang and Darrell Hamilton Solutions for Chapter: Radioactivity, Exercise 2: Exercise 23.2

The equation shows how an isotope of radium decays to become an isotope of radon.

${}_{88}{}^{223}\mathrm{Ra}\to {}_{86}{}^{219}\mathrm{Rn}+{}_2{}^4\mathrm{H}+\mathrm{energy}$

Here, we can check that the equation is balanced by counting the number of nucleons before and after the decay, and the number of protons before and after.

For the nucleons, we have $223=219+4$.

Show that the number of protons is the same before and after the decay.

_____ type of radioactive emission does not change the number of protons or neutrons in the nucleus.

State the type of radioactive emission in which the number of protons in the nucleus changes. Also state whether it increases or decreases.

The equation shows how an isotope of carbon decays to become an isotope of nitrogen.

${}_6{}^{15}\mathrm{C}\to {}_7{}^{15}\mathrm{N}+{}_{-1}{}^0\mathrm{e}+\mathrm{energy}$

Show that this equation is balanced.

What is $A$ and $B$ in the following decay equation, which shows how an isotope of polonium decays to become an isotope of lead:

${}_{84}{}^{211}\mathrm{Po}\to {}_{82}{}^{207}\mathrm{Pb}+A+B$

An isotope of protactinium (symbol $\mathrm{Pa}$) has $91$ protons and $140$ neutrons in its nucleus. Write the symbol for this nuclide.

An isotope of protactinium (symbol $\mathrm{Pa}$) has$91$ protons and $140$ neutrons in its nucleus. The nuclide decays by alpha decay to become an isotope of actinium (symbol $\mathrm{Ac}$). Write a complete decay equation for this decay.

${}_{92}{}^{238}\mathrm{U}$ decays by alpha decay, then beta decay, then beta decay. Deduce the atomic and mass numbers of the daughter nucleus after the third decay and state the element it has become.