Understanding the half-life time of radioactive material using a Half-life calculator

Radioactive decay is a process by which energy is emitted from ionizing radiation. And this radiation, when emitted, is very harmful to all living things and their surroundings. It poses a severe health hazard, damaging the living tissues and changing the DNA structure. The emitted ionizing radiation is nothing but

• alpha particles
• beta particles
• gamma rays

And this Radioactive decay happens only in unstable atoms, called radionuclides, as balanced atoms do not undergo any changes. And these radionuclides have a particular decay rate calculated in terms of "half-life." This is of the main terms used to describe the radioactive decay of a specific sample or element over a predetermined amount of time is the half-life, also known as the half-life period. This half-life can be calculated using a half-life calculator.

How to calculate the half-life using a half-life calculator

Step 1: First, get to know the initial amount of substance N(0)

Step 2: Second, get to know the final amount of substance N(t)

Step 3: Calculate the time the material took to decay in minutes.

Step 4: Give all the above three inputs to your Half-life calculator.

Step 5: You will get your output half-time t1/2, mean lifetime T, and decay constant λ.

If you need more clarification about the half-life calculator working, try using the formula to cross-validate the calculator result.

N(t)=N(0)×0.5(t/T)

N(t)=N(0)×e(−t/τ)

N(t)=N(0)×e(−λt)

τ mean lifetime - the average amount of time a nucleus remains intact; and

λ decay constant (rate of decay).

All the above three are related in the following way:

T =ln(2)/ λ

=ln(2)×τ

Decay constant (λ) = 1/τ

Some radionuclides have a half-life of just a few seconds, while others have between hundreds, millions, or billions of years.

Two common decay chains are

• Uranium-238
• Thorium-232

Half-life period

The duration needed for a quantity to decrease to half its initial value is known as the half-life. This is frequently used to denote how quickly unstable atoms decay radioactively or how long stable atoms last. Additionally, the phrase can be used more broadly to describe any exponential decay.

And to calculate this half-life period, we have this Half-life calculator that produces a value from the three inputs given that use the formula for an atom that undergoes a decaying process to decrease by half.

Three formulas to calculate the exponential decay are

N(t) = No (½) t / t ½

N(t) = No e-t / r

N(t) = Noe λt

where

N0 is the initial quantity

It is the remaining quantity after time, t

t1/2 is the half-life

τ is the mean lifetime

λ is the decay constant

Carbon-14 dating is one of the most well-known half-life applications. Since carbon-14 has a half-life of roughly 5,730 years, it can accurately determine dates up to 50,000 years ago.

William Libby created the carbon-14 dating method based on the fact that carbon-14 is produced continuously in the atmosphere. Photosynthesis is incorporated into plants, and then when animals eat plants, it is incorporated into the animals. The plant or animal dies, and the carbon-14 goes through radioactive decay; therefore, determining the amount of carbon-14 in a sample can tell us when the plant or animal died.

The main reason for calculating this half-life is that they allow you to determine if a sample of a radioactive substance is safe to handle. A sample is deemed safe when its radioactivity is below detection thresholds. Ten half-lives later, something occurs.

The user must feed three data in this half-life calculator to get the desired output.

Quantity remains Nt

Initial quantity N0

Time t

Half-life t1/2

There is yet another calculator to find Half-Life, Mean Lifetime, and Decay Constant Conversion.

Half-life t1/2

Mean lifetime T

Decay constant λ

For Example

An archaeologist identifies a fossil piece with 50% carbon-14 in contrast with another sample. The time of the fossil's death can be known since Nt, N0, and t1/2 are known.

According to formula

N(t) = No (½) t / t ½

t = t1/2 ln (Nt/No)/-ln2

t = 5730ln(50/100)/-0.693

t= 5731

This implies that the fossil that the archaeologist identified is 5731 years old.

This formula can be used to calculate how much of a radioactive isotope is left after a specified number of half-life

Amount remaining=initial amount×(1/2)n

The number of half-lives is n. Even though the number of half-lives is not full, this formula still holds true. And this half-life is used in the application of radiocarbon dating.

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