Half-life and decay

In summary, half-life is the time it takes for half of a radioactive substance to decay. It is important in determining the rate of decay and predicting when a substance will reach a safe level of radioactivity. Half-life is also relevant in nuclear energy production and the management of nuclear waste. Various factors can affect the half-life of a substance, including temperature, pressure, and chemical reactions. Half-life is calculated by measuring the time it takes for half of a substance to decay, often using a Geiger counter. Examples of substances with different half-lives include Uranium-238, Carbon-14, and Iodine-131.
  • #1
Jacobpm64
239
0
(a) The half-life of radium-226 is 1620 years. Write a formula for the quantity, Q, of radium left after t years, if the initial quantity is Q0.

Check me on this one:
Q = (Q0 / 2(1620/t))

(b) What percentage of the original amount of radium is left after 500 years?

Check this one as well:
Q = (Q0 / 21620/500)
Q = (Q0 / 23.24)
Q = Q0 * 2-3.24
Q = Q0(0.1058)
10.6%
 
Physics news on Phys.org
  • #2
In part 'a', the exponent on the 2 should reflect the number of half-lives, which is the ratio of t/T1/2, where T1/2 is the half-life.

So after 1 half-life, Q/Qo= 1/2, and after two half-lives, Q/Qo= (1/2)2 = 1/4, . . .

In the part 'b', the half-life of Rn-226 is 1620 years, the point at which 50% would be remaining, and 500 years is less than 1/3 of the half-life, so does 10.6% look right?
 
Last edited:
  • #3
In other words, you have the exponent "upside down". It should be
t/1620, not 1620/t.
 
  • #4
how's this?

(a) Q = (Q0 / 2t/1620)

(b) Q = (Q0 / 2500/1620)
Q = (Q0 / 20.3086...)
Q = Q0 * 2-0.3086...
Q = Q0(0.8074...)
80.7%
 
  • #5
Better. :approve:
 
  • #6
Do you understand why it is t/1620 rather than 1620/t? The "half life" of a substance is the time it takes to degrade to half its original value. Every time one "half life" passes, the amount is multiplied by 1/2: if the original amount is M, after one "half life" the amount is (1/2)M. After a second "half life", it is (1/2)((1/2)M)= (1/2)2M. After a third "half life" we multiply by 1/2 again: (1/2)((1/2)2M)= (1/2)3M. That is, the exponent just counts the number of "half lives" in the t years. If the "half life" is 1620, that "number of half lives" is t/1620 so the amount will be (1/2)t/1620M= M/2t/1620.
 

1. What is half-life and why is it important?

Half-life is the amount of time it takes for half of a radioactive substance to decay. It is important because it allows us to determine the rate at which a substance decays and the amount of time it will take for the substance to reach a safe level of radioactivity.

2. How does half-life relate to nuclear energy and nuclear waste?

Nuclear energy is produced by the controlled decay of radioactive materials. The half-life of these materials determines the rate at which energy is released. In terms of nuclear waste, the longer the half-life, the longer it will take for the waste to reach a safe level of radioactivity.

3. What factors can affect the half-life of a substance?

The half-life of a substance is determined by its atomic structure and can vary greatly from one substance to another. Factors such as temperature, pressure, and chemical reactions can also affect the half-life of a substance.

4. How is half-life calculated and measured?

Half-life is calculated by determining the amount of time it takes for half of a substance to decay. This can be measured using a Geiger counter, which detects the radiation emitted by the decaying substance.

5. What are some examples of substances with different half-lives?

There are many substances with varying half-lives. Some common examples include Uranium-238 with a half-life of 4.5 billion years, Carbon-14 with a half-life of 5,730 years, and Iodine-131 with a half-life of 8 days.

Similar threads

  • High Energy, Nuclear, Particle Physics
Replies
14
Views
2K
Replies
5
Views
3K
  • Calculus and Beyond Homework Help
Replies
3
Views
3K
  • Calculus and Beyond Homework Help
Replies
1
Views
2K
  • Calculus and Beyond Homework Help
Replies
4
Views
2K
  • Calculus and Beyond Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
2K
  • Biology and Chemistry Homework Help
Replies
2
Views
1K
Back
Top