# Question #5dc62

##### 1 Answer

#### Answer:

Bismuth-214.

#### Explanation:

All you really need to use in order to answer this question is a Periodic Table and the fact that when a radioactive nuclide undergoes **alpha decay**

its,atomic numberdecreases bytwo#color(green)(Z - 2)# its,mass numberdecreases byfour#color(blue)(A - 4)#

This is the case because when a radioactive nuclide undergoes alpha decay, its emits an **alpha particle**, which is essentially the nucleus of a helium-4 atom.

So, grab a Periodic Table and look for astatine,

Astatine has an **atomic number** equal to

#""_(color(white)(1)color(green)(85))^color(blue)(218)"At"#

Since an alpha particle contains **protons** and **neutrons**, you can say that

#""_ (color(white)(1)color(green)(85))^color(blue)(218)"At" -> ""_ color(green)(Z)^color(blue)(A)"?" + ""_ color(green)(2)^color(blue)(4)alpha#

Your goal here is to find the identity of the unknown nuclide, which we labeled as "

As you know, **mass** and **charge** must be conserved in a nuclear reaction. This implies that the **total mass number** and the **total atomic number** must be **equal** on both sides of the equation.

You can thus say that

conservation of mass# ->" "color(blue)(218 = A + 4)#

conservation of charge# -> " "color(green)(85 = Z + 2)#

This will get you

#color(blue)(A = 218 - 4 = 214)" "# and#" "color(green)(Z = 85 - 2 = 83)#

Check the Periodic Table for the element that has an atomic number equal to

#""_ color(green)(Z)^color(blue)(A)"?" = ""_ (color(white)(1)color(green)(83))^color(blue)(214)"Bi"#

Therefore, you can say that the alpha decay of astatine-218 will produce bismuth-214, or

The complete nuclear equation will be

#""_ (color(white)(1)color(green)(85))^color(blue)(218)"At" -> ""_ (color(white)(1)color(green)(83))^color(blue)(214)"Bi" + ""_ color(green)(2)^color(blue)(4)alpha#