# Question #4a5cf

Dec 28, 2016

#### Explanation:

Polonium-212 undergoes alpha decay to produce lead-208, which means that it gives off alpha radiation, i.e. alpha particles.

An alpha particle, $\alpha$, is simply the nucleus of a helium-4 atom, which means that it contains

• two protons
• two neutrons

When a radioactive nuclide emits an alpha particle

• its mass number will decrease by $4$

The mass number, $A$, is given by the number of protons and neutrons, and so

$A = \text{2 protons " + " 2 neutrons} = 4$

• its atomic number will decrease by $2$

The atomic number, $Z$, is given by the number of protons, and so

$Z = \text{2 protons} = 2$

Now, the two elements that you're working here with have

$\text{Po: " {(A = 212),(Z = 84) :}" }$ and $\text{ " "Pb: } \left\{\begin{matrix}A = 208 \\ Z = 82\end{matrix}\right.$

This confirms that you're dealing with an alpha decay because the balanced nuclear equation that describes this process looks like this

${\text{_ (color(white)(1)color(darkgreen)(84))^color(blue)(212)"Po" -> ""_ (color(white)(1)color(darkgreen)(82))^color(blue)(208)"Pb" + }}_{\textcolor{\mathrm{da} r k g r e e n}{2}}^{\textcolor{b l u e}{4}} \alpha$

Notice that mass and charge are conserved, since

$\textcolor{b l u e}{212 = 208 + 4} \to$ conservation of mass

$\textcolor{\mathrm{da} r k g r e e n}{84 = 82 + 2} \to$ conservation of charge