Solving Radioactive Decay: Half-Life, Muons & Lorentz Transformation

In summary, the conversation discusses the topic of radioactive decay and its application in an experiment involving cosmic ray muons. The participants discuss the half-life of muons, their speed, and how to calculate their flight time. They also mention using logarithms to manipulate the equation for the decay law. The conversation ends with a resource suggestion for basic math tips.
  • #1
timothy123
4
0
[SOLVED] Radioactive decay

Hi guys, this is just a basic maths incompetency. I hope someone can guide me forwards! (Slack biology student, delving into physics)

Cosmic ray muons decay with a half-life of 1.53 x 10-6 s. During an experiment 563 +/- 10 muons are counted at the top of Mount Washington, an altitude of 6265 ft. When the same apparatus is moved to an altitude of 10 ft the number of muons detected falls to 408 +/- 9, over the same time period.

(a) Given that the speed of the muons is 0.992c determine the flight time, Tf, ( 1 metre = 3.28 ft )

(b) Using the appropriate decay law find the time of flight as measured from the muon ‘clock’, Tm, and determine the ratio Tm/Tf.

(c) Compare this with the value predicted by the appropriate Lorentz transformation and comment.



http://img168.imageshack.us/img168/2086/hlkb7.png [Broken],[/URL] where N(t) is the number left at time 't', No the original number and T the half life.


I can do (a) with no problems, and thus I can probably do the latter half of (b) and (c) without issue. My stumbling point is in actually rearranging the above equation to isolate the term I want. I have this:
http://img410.imageshack.us/img410/3239/hlea6.png [Broken]

- but I don't know how to get 't' where I want it! I've been googling how to manipulate powers properly, but no joy. What can I say... no maths since I was 16! :-)

Cheers all.

Tim
 
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  • #2
You'll want to take the logarithm to base 2 of both sides.

More info: http://www.counton.org/alevel/pure/purtutloglaw.htm [Broken]
 
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  • #3
Kurdt said:
You'll want to take the logarithm to base 2 of both sides.

More info: http://www.counton.org/alevel/pure/purtutloglaw.htm [Broken]

Thanks Kurdt. A much-appreciated pointer.

Does that mean that the following is true?:
http://img259.imageshack.us/img259/7027/screenshot3ch4.png [Broken]

It was this youtube video that took me there... http://youtube.com/watch?v=OS-EnAFKWpI
Seems like a great resource for basic maths tips.
 
Last edited by a moderator:
  • #4
Nice video. Yes you are correct.
 

1. What is radioactive decay?

Radioactive decay is the process by which unstable atoms release energy and particles in order to become more stable. This can happen through the emission of alpha or beta particles, or through the release of gamma rays.

2. What is half-life?

Half-life is the amount of time it takes for half of a radioactive substance to decay. It is a constant for each type of radioactive element and can be used to determine the rate of decay.

3. How do muons play a role in radioactive decay?

Muons are subatomic particles that are created when cosmic rays from outer space collide with particles in Earth's atmosphere. These muons can interact with atomic nuclei, causing them to undergo radioactive decay.

4. What is the Lorentz transformation and how does it relate to radioactive decay?

The Lorentz transformation is a mathematical formula that describes how time, distance, and mass change for objects moving at high speeds. It is important in the study of radioactive decay because it helps scientists understand how particles decay at different velocities.

5. How is radioactive decay used in scientific research?

Radioactive decay is used in a variety of scientific fields, including geology, archaeology, and medicine. By studying the rate of decay of radioactive elements, scientists can determine the age of objects or materials, track the movement of particles in experiments, and even diagnose and treat diseases.

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