AP Chemistry : Elements, Ions, and Isotopes
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Example Question #2 : Radioactive Decay And Nuclear Chemistry
The isotope 
In order for the nuclear reaction to be balanced 
β radiation
an electron
either an electro or β radiation
a proton
either an electro or β radiation
A beam of electrons is known also as β radiation. An electron has atomic number of 
Where 
Example Question #2 : Radioactive Decay And Nuclear Chemistry
Suppose that a radioactive isotope whose half-life is equal to 
In order to answer this question, we'll need to employ the equation for first-order decay. The reason we know that this is a first order decay process is because we are told that the compound in question is radioactive. It's important to recall that all radioactive decay processes occur via a first order decay mechanism.
Before jumping into the math, let's first make a quick ballpark prediction of where our answer should be. We know that the half-life for any compound is the amount of time it takes for half of that compound to decay. Furthermore, we're given the value for a compound's half-life. Since the amount of time that has passed in the question is less than the half-life, we would expect to still have over half of the compound left. Thus, our answer should be above 
Where 
To solve for the fraction of compound that exists at a given time relative to the initial amount, we can make the following changes to the above equation.
Thus far, we have everything we need except for the decay constant. However, as long as we know the half life of the compound, we can calculate the decay constant using the following formula that applies to all first order reactions.
Notice that the above decay constant has units of inverse-time. This is what we would expect, since all first order reactions have rate constants with these units.
Now, we are ready to plug in the value we calculated for the decay constant into the rate equation to find our answer.
Going back to the quick prediction we made, we can see that this calculated value agrees with our prediction.
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