Science Time   
                                                                                                                                                      Last updated:  07/19/2010


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Writing a nuclear reaction equation

In order to write an equation for a nuclear reaction, we must first establish some basic rules. Each of the elements involved in the reaction is identified by the chemical symbol. Two numbers are attached to the symbol. The number at the upper right is the mass number, also known as the ‘A’ number. The 'A' number describes the atomic weight of the atom and identifies the number of protons and neutrons in the nucleus. The number at the lower left is the atomic number, or ‘Z’ number. The 'Z' number describes the number of protons in the nucleus and determines the type of atom.

example: The symbol for Uranium-238 is 92U238

This shows you that Uranium has a mass number of 238 and an atomic number of 92.

Common symbols you need to utilize in equation writing:

The symbol for an alpha particle = 2He4
The symbol for a beta particle is –1e0.
The chemical symbol for a neutron = 0n1
The chemical symbol for gamma radiation =  γ
 
Word Problem:
1.  Uranium-238  isotope undergoes alpha decay to produce Thorium and gamma rays.
Express this in an equation.
            answer:   92U238    →  90Th234  +  2He4   +  γ

 
1.  Alpha Decay

A helium nucleus is given off as the parent (original) element is transmuted.
Basic format:  88Ra226 (parent element) → ? (daughter element) +  2He4  (helium nucleus)

To determine the daughter element's mass number, subtract 4 from the parent element's
mass number (this represents the amount of mass lost during the a decay process).  I
n this particular case, the daughter element's mass is 226 - 4 = 222.

To determine the daughter element's atomic number, subtract 2 from the parent
element's atomic number (the number of protons lost during the alpha decay process). 
In this case, the daughter element's atomic number is 88 - 2 = 86.

The element formed in the alpha decay process is therefore 88Ra226 and the complete
nuclear equation for this process :  88Ra226 →  86Rn222   +  2He4  
 

2.  Beta Decay

An electron (b particle) is given off as the parent (original) element is transmuted.
Basic format:  15P34 (parent element) →? (daughter element) + –1e0 (beta particle, or electron)

  No mass is lost in a beta decay, so the daughter element has the same mass
number as the parent element.  In this particular case, the daughter element's
mass number is 34.

  To determine the daughter element's atomic number, add 1 to the parent element's
atomic number (the number of protons formed during the beta decay process). 
In this case, the daughter element's atomic number is 15 + 1 = 16.

  The element formed in the beta decay process is therefore 34/16S, and the
 complete nuclear equation for this process is:    15P34  →    16S 34    +   –1e0  

3.  Gamma Decay

In gamma decay, a ray is given off.  Since a gamma ray has no mass, its formation causes no transmutation of the original element.  It may accompany either an alpha or a beta decay, in which case you use the appropriate rules above to determine the daughter element formed.