Solving a Half-Life Physics Problem: Estimating Radon-222 Atom Decay in 12 Days

In summary, Radon-222 is a radioactive gas with a half-life of 3.82 days. A gas sample containing 4.5*10^8 radon atoms initially will have half of its atoms decay after 3.82 days. After 12 days, there will be \frac{4.5 \ast 10^8}{2^3} or approximately 56250000 radon atoms remaining.
  • #1
mustang
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Radon-222 is a radioactive gas with a half-life of 3.82 days. A gas sample contains 4.5*10^8 radon atoms initially.
Estimate how many radon atoms will remain after 12 days.
This Is what i have done:
3.82 days=3.82*24*60*60=330048seconds
what's next?
 
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  • #2
12 days is how many half-lives? What does half-life mean? How much is left after one half-life? Two half-lives?
 
  • #3
You don't need seconds. After one half-life, you're dividing by 2. If you determine how many half-lifes are in 12 days, you'll know how many times to divide by 2.

As an example, if you divided by 2 twice, you would have:

[tex]\frac{4.5 \ast 10^8}{2 \ast 2}[/tex]

or

[tex]\frac{4.5 \ast 10^8}{2^2}[/tex]

If dividing by 2 three times:

[tex]\frac{4.5 \ast 10^8}{2 \ast 2 \ast 2}[/tex]

or

[tex]\frac{4.5 \ast 10^8}{2^3}[/tex]

The power in the denominator is however many times you want to divide by 2 and doesn't have to be an integer.
 

1. What is the Half-Life physics problem?

The Half-Life physics problem is a theoretical problem in physics that seeks to explain the decay of unstable particles over time. It is named after the concept of half-life, which is the amount of time it takes for half of a substance to decay.

2. Why is the Half-Life physics problem important?

The Half-Life physics problem is important because it helps us understand the fundamental principles of particle decay and the behavior of unstable particles. It also has practical applications in fields such as nuclear physics, radiocarbon dating, and medical imaging.

3. How is the Half-Life physics problem solved?

The Half-Life physics problem is solved using mathematical equations and models, such as the exponential decay equation and the decay constant. These equations take into account the initial amount of the substance, the rate of decay, and the half-life to calculate the amount of the substance remaining at any given time.

4. What factors can affect the Half-Life of a substance?

The Half-Life of a substance can be affected by various factors, such as temperature, pressure, and the chemical composition of the substance. For example, increasing the temperature can speed up the decay process, while changing the chemical makeup of the substance can alter its decay rate.

5. How does the Half-Life physics problem relate to nuclear reactions?

The Half-Life physics problem is closely related to nuclear reactions, as it helps us understand how unstable particles, such as radioactive isotopes, decay and transform into more stable elements. This knowledge is crucial in predicting and controlling nuclear reactions, as well as in developing nuclear technologies such as nuclear power and weapons.

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