Radioactive substances decay over time
Radioactive substances decay over time. A certain radioactive substance has a half-life of 4 days, i.e. after 4 days only half of the original amount of substance is present.
Use the following formula;
f(t)=b*a^t,
1/2*b=b*a^t
I already have the following;
Growth factor, a=0.841
b = the initial factor
1/2*b = the half of the initial factor
Question;
c) What fraction of the initial amount of substance is still present after 2,3,4,6,8,10 days? (Prepare a table)
Sample Solution
You are correct that the half-life of a radioactive substance is the time it takes for half of the original amount of substance to decay. In this case, the half-life is 4 days. This means that after 4 days, only half of the original amount of substance will be left.
You are also correct that the formula f(t)=b*a^t can be used to calculate the amount of radioactive substance remaining after a certain amount of time (t). In this formula, b is the initial amount of substance, a is the growth factor, and t is the time in days.
Full Answer Section
We know that the initial amount of substance is b, and we know that the growth factor is 0.841. We also know that after 4 days (t=4), half of the original amount of substance will be left. This means that the amount of substance remaining after 4 days is 1/2*b. We can plug these values into the formula to get the following equation: 1/2*b = b * 0.841^4 Simplifying the right side of the equation, we get: 1/2 = 0.841^4 Taking the fourth root of both sides of the equation, we get: t = 4 This confirms that the half-life of the radioactive substance is 4 days. I hope this helps! Here are some additional things to keep in mind:- The growth factor in the formula f(t)=b*a^t is always less than 1. This is because radioactive substances decay over time, not grow.
- The half-life of a radioactive substance is a constant value. This means that the amount of time it takes for half of the substance to decay will always be the same, no matter how much of the substance there is to start with.