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Half Life Formula

Half-life is a particular phenomenon that takes place every day in various chemical reactions as well as nuclear reactions. One can get an idea about half-life by imagining a situation in which an individual watches a movie in a theatre. This individual is eating from a tub of popcorn. After about 15 minutes, half the popcorn is over. The rest of the popcorn continues until the rest of the movie. Most noteworthy, this shows that the rate of popcorn eating was not at a steady pace and that the half-life of popcorn is of 15 minutes. Learn the half life formula here in an easy way.

Half Life Formula

What is Half Life?

Half-life means the amount of time that some element takes for half of its particular sample to react. Furthermore, it refers to the time that a particular quantity requires to reduce its initial value to half. This concept is quite common in nuclear physics and it describes how quickly atoms would undergo radioactive decay.

Moreover, it could also mean how long the atom would survive radioactive decay. Also, the half-life can facilitate in characterizing any type of decay whether exponential or non-exponential. A good example can be that the medical sciences refer to the half-life of drugs in the human body which of biological nature.

half life formula

During the natural process of radioactive decay, all atoms of an element are not instantaneously changed to atoms of another. This decay process takes time and there is value in being able to express the rate at which a process occurs. A useful concept is a half-life, which is the time required for half of the starting material to change or decay. Half-lives can be calculated from measurements on the change in mass of a nuclide and the time it takes to occur.

Here, we know that the time of any substance’s half-life is the time for the disintegration of half of the original nuclei. Although chemical changes may speed up or slow down by changing factors such as temperature, concentration, etc but these factors will not affect the half-life. Each radioactive element will have its own unique half-life and it is independent of any of other factors.

The Formula for Half-Life

We can describe exponential decay by the following given decay equation:

\(t_{\frac{1}{2}}=\frac{ln2}{\lambda}=\frac{0.693}{\lambda}\)

Where,

\(t\ _{\frac{1}{2}}\) The half-life of the substance
\(\lambda\) The disintegration constant or decay constant.

Also, ln(2) happens to be the natural logarithm of 2 and equals approximately 0.693.

Solved Examples for Half Life Formula

1: Calculate the half-life of a radioactive substance whose disintegration constant happens to be 0.002 per year?

Solution: The quantities available here are,

\(\lambda = 0.002 per year\)

Consequently, the half-life equation becomes:

\(t_{\frac{1}{2}}=\frac{ln2}{\lambda}=\frac{0.693}{\lambda} \\\)

\(t_{\frac{1}{2}}=\frac{ln2}{\lambda}=\frac{0.693}{0.002} \\\)

\(t_{\frac{1}{2}} = 346.5 \; years\)

Hence, the half-life of this particular radioactive substance will be 346.5 years.

Example-2: If the half-life of 100.0 grams of a radioactive element is 8 years. Then how many grams will remain after 32 years?

Solution: To answer this question, there is no need to solve the radioactive decay equation. Obviously

\(\frac{32}{8} = 4,\)

Then the material will go through 4 half-lives.

Thus, \(100.0 g \rightarrow 50.0 g \rightarrow 25.0 g \rightarrow 12.5 g \rightarrow 6.25 g.\)

Therefore, after 32 years 6.25 g will remain.

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