How Many Half-Lives Are Needed for Specific Decay Percentages?

In summary, the question is asking how many half-lives are needed for (a) 90% and (b) 99% of a radioactive sample to decay. The relevant equations are N=No(1/2)^(t/t1/2) and N=No(1/2)^n, where t/t1/2 represents the number of half-lives (n) and N/No is the ratio of the final number of atoms to the initial number. The solution involves finding the value of n, which can be calculated from the given ratios.
  • #1
Sarah88
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Homework Statement



How many half-lives must elapse until (a) 90% and (b) 99% of a radioactive sample of atoms has decayed?


Homework Equations



N=No(1/2)^(t/t1/2)
N=No(1/2)^(n)

The Attempt at a Solution



The part of the solution I don't understand is how to get the second equation N=No(1/2)^n from N=No(1/2)^(t/t1/2). In other words, why is t/t1/2 grouped into the variable "n" if we don't know the value for t or the half life? Thank you!
 
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  • #2
Question asks about "how many half lives", t/t1/2 is just that - number of half lives.
 
  • #3
The number of half-lives (n) is the question. You do not know the half life, but you can calculate n from the ratio of N/No.

ehild
 
  • #4
Ok, that makes a lot more sense, thank you!
 
  • #5


The second equation, N=No(1/2)^n, is a simplified version of the first equation, N=No(1/2)^(t/t1/2). The variable "n" represents the number of half-lives that have passed, and it is used to simplify the equation. The value for t or the half-life is not necessary to solve for the number of half-lives, as long as we know the initial number of atoms (No) and the current number of atoms (N). We can determine the value of n by taking the logarithm of both sides of the equation and solving for n. I hope this helps clarify the equation for you.
 

Related to How Many Half-Lives Are Needed for Specific Decay Percentages?

1. What is nuclear decay?

Nuclear decay is the process in which an unstable atomic nucleus releases energy in the form of radiation, resulting in the formation of a more stable nucleus.

2. What is a half-life?

A half-life is the amount of time it takes for half of the radioactive atoms in a sample to decay into a more stable form. It is a constant rate characteristic of each type of radioactive material.

3. How is half-life used in radioactive dating?

By measuring the amount of radioactive material and its half-life, scientists can determine the age of a material or artifact through a process called radioactive dating. This is based on the principle that the amount of radioactive material decreases over time, allowing for the calculation of how much time has passed since the material was formed.

4. What are the types of nuclear decay?

There are three main types of nuclear decay: alpha decay, beta decay, and gamma decay. Alpha decay involves the release of an alpha particle, which consists of two protons and two neutrons. Beta decay involves the release of a beta particle, which can be either an electron or a positron. Gamma decay involves the release of gamma rays, which are high-energy photons.

5. How is nuclear decay used in practical applications?

Nuclear decay has many practical applications, including in the fields of energy production, medical imaging and treatments, and carbon dating. Nuclear power plants use controlled nuclear decay to produce electricity, while medical professionals use it for diagnosing and treating diseases. Carbon dating uses the predictable rate of decay of carbon-14 to determine the age of organic materials.

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