# Radioactive Decay: Finding the Half-Life of K-40 in KCL

• JingXionG
In summary, the conversation discusses finding the half-life of a radioactive sample of KCL, which is decaying at a constant rate of 4490 Bq. The decays are traced to the isotope K-40, which makes up 1.17% of normal potassium. After finding the number of K-40 atoms in the sample, the decay constant is calculated and used to determine the half-life, which is equivalent to 1.25 billion years. It is noted that this method may not be completely rigorous for shorter half-lives.
JingXionG
A 2.71g sample of KCL is found to be radioactive, and it is decaying at a constant rate of 4490 Bq. The decays are traced to the ekement potassium and in particular to the isotope K(proton number 40), which constitutes 1.17% of normal potassium. find the half-life of this nuclide( Take molar mass of KCL = 74.555g)

Ans provided is 1.25 x 10^9 years. I can't seem to even come close to that value.

I found the number of K-40 in the sample which is 2.560 x 10^20. From there, using A= constant x number of particles of K-40 and rate of decay = -dN/dt, I can't seem to get that ans

I think you're on the right track here. Your number for the number of 40K atoms is very close to what I got.

My next step was to find the decay constant, [lambda]. If the rate of decay is constant, then

[lambda] = decays per second / number of atoms

4490 Bq = 4490 decays per second. Once you have [lambda], you can use

T1/2 = ln(2) / [lambda] to get your half-life in seconds. I get 3.95 x 10 16 seconds, which is equivalent to 1.25 Billion years.

I should add a word of caution that this is *not* a completely rigorous method. You can't use it for something with a half-life of, say, 15 seconds. However, since the problem states the decay rate is constant and you can see that the decays/second are << than the number of atoms in the sample (16 orders of magnitude in this case), it should get an accurate answer.

argh

i know where i went wrong, forgot to convert the seconds to years!

## 1. What is radioactive decay?

Radioactive decay is the process by which unstable atoms release energy and particles in order to become more stable. This process can result in the formation of new elements or isotopes.

## 2. How does radioactive decay occur?

Radioactive decay occurs due to the inherent instability of certain atoms, known as radioactive isotopes. These atoms have an excess of either protons or neutrons in their nucleus, making them unstable. In order to become more stable, these atoms release energy and particles, which is known as radioactive decay.

## 3. What are the different types of radioactive decay?

There are three main types of radioactive decay: alpha, beta, and gamma decay. Alpha decay involves the emission of an alpha particle (two protons and two neutrons) from the nucleus. Beta decay can occur in two forms: beta-minus decay, which involves the emission of an electron, and beta-plus decay, which involves the emission of a positron. Gamma decay involves the emission of a high-energy photon.

## 4. How is radioactive decay measured?

The rate of radioactive decay is measured using the half-life of a radioactive isotope. The half-life is the amount of time it takes for half of the atoms in a sample of a radioactive isotope to undergo radioactive decay. This measurement is important in fields such as radiometric dating and nuclear medicine.

## 5. What are the applications of radioactive decay?

Radioactive decay has many practical applications, including radiometric dating to determine the age of rocks and fossils, medical imaging and treatment in nuclear medicine, and power generation in nuclear reactors. It also plays a vital role in understanding the processes of the Earth's formation and evolution.

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