ChemTeam: Writing Nuclear Reactions: Converting Between the Long and the Short Form

Writing Nuclear Reactions
Converting Between the Long and the Short Form

Writing Nuclear Equations: Five Examples      Writing Fission Equations
Writing Nuclear Equations: Ten Examples      Writing Fusion Equations
Writing Nuclear Equations: Fifteen Examples      Radioactivity Menu

Just about every nuclear reaction can be written in a long form and a short form. This tutorial is about how to convert from one to the other.

A Brief Tutorial About Writing Nuclear Symbols

Example #1: This is a long form:

$_{29}^{63} Cu$ + $_{1}^{2} H$ ---> $_{30}^{63} Zn$ + 2 $_{0}^{1} n$

And, the same reaction in short form:

$_{29}^{63} Cu$ (d, 2n) $_{30}^{63} Zn$

How to convert? Well, consider these questions:

(a) See that comma in the short form? See that arrow in the long form?
(b) See that parenthesis to the left in the short form? See that plus sign on the reactant side?
(c) See that parenthesis to the right in the short form? See that plus sign on the product side?

Think of each set as being equivalent. The comma and the arrow play equivalent roles. The left parenthesis and the reactant plus sign each play the same role. The right parenthesis and the product plus sign eachnplay the same role.

That means the d is on the reactant side and the 2n is on the product side. The d stands for deuterium ( $_{1}^{2} H$ ) and the n stands for neutron.

By the way, t will stand for tritium ( $_{1}^{3} H$ ) and p will stand for protium ( $_{1}^{1} H$ ). Protium is the name of the lightest of the three hydrogen isotopes. Often, it's just called hydrogen, but in nuclear reactions, it's called protium.

Example #2: Once again, a long form:

$_{41}^{93} Nb$ + $_{2}^{4} He$ ---> $_{43}^{96} Tc$ + $_{0}^{1} n$

And, its short form:

$_{41}^{93} Nb$ (α, n) $_{43}^{96} Tc$

Remember that this:

(α, n)

is equivalent to this:

+ $_{2}^{4} He$ ---> + $_{0}^{1} n$

Notice how the neutron will not be written first on the product side. There is somewhat of an unwritten rule that you write each side with the heaviest first, then the lightest.

The α stands for the alpha particle. In standard isotopic notation, the alpha particle is $_{2}^{4} He$ .

A few more you will see:

Name      letter      isotopic notation
beta particle     β or β¯               $_{−1}^{0} e$
positron        β⁺               $_{+1}^{0} e$
gamma        γ              none

Example #3: Sometimes, you have to use the full isotopic notation inside the parentheses. Here's the long form:

$_{98}^{252} Cf$ + $_{5}^{10} B$ ---> $_{103}^{259} Lr$ + 3 $_{0}^{1} n$

Convert it to the short form.

Solution:

1) A short form template:

_____ (_____, _____) ______

2) Write the heavier of the two reactants:

$_{98}^{252} Cf$ (_____, _____) ______

3) Write the lighter of the two reactants:

$_{98}^{252} Cf$ ( $_{5}^{10} B$ , _____) ______

4) Write the lighter of the two products:

$_{98}^{252} Cf$ ( $_{5}^{10} B$ , 3n) ______

5) Write the heavier of the two products:

$_{98}^{252} Cf$ ( $_{5}^{10} B$ , 3n) $_{103}^{259} Lr$

Example #4: Write the short form of this nuclear reaction.

$_{30}^{64} Zn$ + $_{−1}^{0} e$ ---> $_{29}^{63} Cu$ + $_{0}^{1} n$

Solution:

1) Here's the entire short form:

$_{30}^{64} Zn$ (β¯, n) $_{29}^{63} Cu$

2) Notice the use of β¯ for the electron. Some sources will use the beta without the minus, as in β. It is the ChemTeam's preference to include the minus sign.

Writing Nuclear Equations: Five Examples	Writing Fission Equations
Writing Nuclear Equations: Ten Examples	Writing Fusion Equations
Writing Nuclear Equations: Fifteen Examples	Radioactivity Menu

Name	letter	isotopic notation
beta particle	β or β¯	$_{−1}^{0} e$
positron	β⁺	$_{+1}^{0} e$
gamma	γ	none

Writing Nuclear ReactionsConverting Between the Long and the Short Form

Writing Nuclear Reactions
Converting Between the Long and the Short Form