# Fill in the blank in each of the following nuclear equations. You will need to enter either a form of radiation or an isotope. If it is the latter, you must fully identify the isotope in superscript/subscript notation?

## Jun 1, 2018

A. ${\textcolor{w h i t e}{l}}_{10}^{23} \text{Ne" to color(white)(l)_11^(23)"Na} + {e}^{-}$

B. ${\textcolor{w h i t e}{l}}_{94}^{242} \text{Pu" to color(white)(l)_2^(4)"He" + color(white)(l)_92^(238)"U}$

C. ${\textcolor{w h i t e}{l}}_{84}^{204} \text{Po" + e^(-) to color(white)(l)_83^(204)"Pb}$

#### Explanation:

Equation A describes a neon-23 atom undergoing radioactive decay; a sodium atom of the same mass number $A = 23$ is formed as the product; however the proton number $Z$ decrease by $1$. A drop in $Z$ without any changes in $A$ indicates that some weak interactions must have been taken place.

The beta-plus decay process, in which a neutron converts to a proton while emitting an electron, is likely to be accountable for this observation:

${\textcolor{w h i t e}{l}}_{0}^{1} {\text{n"^0 to color(white)(l)_1^(1)"p}}^{+} + {e}^{-}$

Optional: Check for the conservation of charge in this equation:

$\text{L.H.S."=0=1+(-1)="R.H.S.}$

Note that this problem does not state the charge on each of the species. It is, therefore, necessary to check $A$ and $Z$ numbers when completing the equation.

color(white)(l)_10^(23)"Ne" to color(white)(l)_11^(23)"Na" + ul(color(black)("x"))

$\text{x}$ should carry a nucleon number of $0$ and a baryon number of $- 1$; what is $x$?

In the second equation B., plutonium 242 undergoes alpha decay and emits an alpha particle (helium 4 nucleus ${\textcolor{w h i t e}{l}}_{\textcolor{p u r p \le}{2}}^{\textcolor{n a v y}{4}} \text{He}$.) As a result, the $\text{A}$ number of the product nuclei shall be lower than the parent nuclei by $\textcolor{n a v y}{4}$ and the $\text{Z}$ number lower by $\textcolor{p u r p \le}{2}$.

${\textcolor{w h i t e}{l}}_{94}^{242} \text{Pu" to color(white)(l)_2^(4)"He" + color(white)(l)_92^(238)"X}$

The product should, therefore, contain $238$ nucleons and $92$ protons. What is the symbol for this element?

In the third equation C., polonium 204 undergoes electron capture to convert a proton into a neutron.

${\textcolor{w h i t e}{l}}_{1}^{1} {\text{p"^(+) + e^(-) to color(white)(l)_0^(1)"n}}^{0}$

... which is nearly the same as the beta decay process, reversed. As a weak interaction process, the nucleon number of the product will be identical to that of the parent nuclei; the proton number, however, will decrease by $1$ as one of the protons got converted to a neutron.

${\textcolor{w h i t e}{l}}_{84}^{204} \text{Po" + e^(-) to color(white)(l)_color(purple)(83)^(204)"X}$

which element does $\text{X}$ represent?