Radioactive Decay & Nuclear Physics: half-life simulator

 

Radioactive Decay

Radioactive substances such as Uranium and Radium spontaneously disintegrate while emitting radiation in the form  of α or ß particles and γ rays.

The loss of an alpha particle result in the formation of a new element,  that occupy a position on the Periodic Table, two places to the left of  the parent element. The loss of a beta particle, on the other hand, leads  to the formation of an element that occupies a position one place to the right on the Periodic Table.

The loss of an alpha particle or beta particle leaves the nucleus in question with an excess amount of energy. The nucleus tends to emit gamma rays to get rid of the excess energy.

Half-Life

The time taken by a radioactive substance to lose half of its mass / nuclei is called the half life of the substance.

E.g.

The half-life of C-14, the radioactive form of carbon, is about 5740 years.

That means, 100 g of Carbon-14 will become 50 g in 5740 years. C-14, however, is often exists with the most common carbon isotope, C-12.

The half-life of Uranium-238 is approximately 4.468 billion years. Uranium-235 has a shorter half-life of about 700 million years. They are found in rocks and minerals; their respective half-life can be used to determine the age of them.

Technetium-99m, a medial radioisotope, has a half-life of just 6 hours, because they are used inside the body to diagnose certain illnesses; since half-life is very short, they decay quickly without exposing the patient to harmful radiation within the body. Iodine-131, another medical isotope, has a half-life of 8 days.

Worked Example

The half-life of a  radioactive substance is 5 days. A sample of mass 1024 g shows radioactive decay. Find the mass of the substance left after,

1. 5 days
2. 10 days
3. 4 half-lives
4. Hence find an expression for the remaining mass in n half-lives.

1. 512 g
2. 256 g
3. 46 g
4.  

    Mo → Mo/2→ Mo/4 → Mo/8 → ....... → Mn

    Mo → Mo/2¹→ Mo/2² → Mo/2³ → ....... → Mo/2ⁿ

    Mn = Mo(1/2)ⁿ

With the following fully interactive simulation, you can practise radioactive decay:

You can change the initial mass - Mo

You can change the half-life

You can change the number of half-lives