Half-life of radioactive substance

In summary, the half-life of a radioactive substance is the amount of time it takes for half of the initial amount of the substance to decay. It is determined by measuring the rate of decay over a period of time and is a constant value unique to each substance. The concept of half-life is important in predicting the rate of decay and has applications in various fields. A shorter half-life indicates less stability and a quicker decay, while a longer half-life indicates greater stability and a slower decay rate. However, the overall stability of a substance is also influenced by factors such as the type of decay and energy of emitted particles.
  • #1
gmmstr827
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1

Homework Statement



If 20% of a radioactive substance disappears in 70 days, what is its half-life?

Homework Equations



y = C*e^(k*t)
where t is time in days
k is the constant of proportionality?
y is the current amount of substance


The Attempt at a Solution



20% disappears, so 100% - 20% = 80% remaining = 0.80 after 70 days
.8*C = C*e^(70*k)
Solve for k
k = -3.188 * 10^-3

Plug k value back into equation to find t at the substance's half-life (.5)
.5*C = C*e^((-3.188 * 10^-3)*t)
Solve for t
t = 217.44

217.44 days is the substance's half-life.

Is that correct?
Thank you.
 
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  • #2
It matches what I get.
 

1. What is the half-life of a radioactive substance?

The half-life of a radioactive substance is the amount of time it takes for half of the initial amount of the substance to decay. This is a constant value that is unique to each radioactive element.

2. How is the half-life of a radioactive substance determined?

The half-life of a radioactive substance is determined by measuring the rate of decay of the substance over a period of time. This can be done through various methods such as counting the number of particles emitted or measuring the decrease in radioactivity.

3. Can the half-life of a radioactive substance change?

No, the half-life of a radioactive substance is a constant value that does not change. It is a property of the substance itself and is not affected by external factors.

4. Why is the concept of half-life important in radioactive decay?

The concept of half-life is important because it allows us to predict the rate of decay of a radioactive substance. This is crucial in various fields such as nuclear energy, medicine, and environmental science.

5. How does the half-life of a radioactive substance affect its stability?

A shorter half-life indicates that a substance is less stable and will decay more quickly, while a longer half-life indicates greater stability and a slower rate of decay. However, the half-life alone does not determine the overall stability of a substance, as other factors such as the type of decay and energy of the emitted particles also play a role.

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