Last updated on August 2nd, 2025
In nuclear physics and chemistry, the half-life is a measure of the time it takes for half of a given amount of a radioactive substance to decay. Understanding the half-life formula is crucial for calculations in these fields. In this topic, we will learn the formula for half-life and its applications.
The half-life formula is used to determine the decay rate of radioactive substances. Let’s learn the formula to calculate the half-life.
The half-life is the time required for half of a radioactive substance to decay.
It is calculated using the formula: [ t_{1/2} = frac{ln(2)}{lambda} ] where ( lambda ) is the decay constant.
In physics and chemistry, the half-life formula is essential for understanding radioactive decay and its applications.
Here are some important aspects of the half-life formula:
Students often find mathematical formulas challenging.
Here are some tips and tricks to master the half-life formula:
In real life, the half-life formula plays a major role in various fields.
Here are some applications of the half-life formula:
Students make errors when calculating half-life. Here are some mistakes and the ways to avoid them to master this concept.
If a radioactive substance has a decay constant of 0.693 per year, what is its half-life?
The half-life is 1 year.
Using the formula
( t_{1/2} = frac{ln(2)}{lambda} ), where ( ln(2) approx 0.693 ) and ( lambda = 0.693 ),
we get: [ t_{1/2} = frac{0.693}{0.693} = 1 { year} ]
A radioactive isotope has a half-life of 5 years. What is the decay constant?
The decay constant is approximately 0.139 per year.
Using the formula ( t_{1/2} = frac{ln(2)}{lambda} ), we rearrange to find ( lambda ):
[ lambda = frac{ln(2)}{t_{1/2}} = frac{0.693}{5} approx 0.139 { per year} ]
If a sample initially has 80 grams and after 10 years it has 20 grams, what is the half-life?
The half-life is approximately 5 years.
The substance decays from 80 grams to 20 grams, which means it has gone through two half-lives (80 to 40 to 20).
Since this process took 10 years, each half-life is ( frac{10}{2} = 5 ) years.
A substance's half-life is 3 years. How much of a 100g sample remains after 6 years?
25 grams remain.
After one half-life (3 years), 50 grams remain.
After another half-life (6 years total), half of that remains, which is 25 grams.
Calculate the half-life if a substance decays with a decay constant of 0.231 per day.
The half-life is approximately 3 days.
Using the formula ( t_{1/2} = frac{ln(2)}{lambda} ), where ( lambda = 0.231 ),
we get: [ t_{1/2} = frac{0.693}{0.231} approx 3 { days} ]
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