Half-Life
Half-Life is the time period in which the radioactive substance goes through the process of radioactive decay and disintegrates into smaller more stable substances until its concentration remains half of the initial concentration. This time period is represented by t1/2 and as it is time, the unit of half-life is the same as time i.e., second, minute, hour, day, or year.
Half-Life Formula
Half-life can be calculated using the division of λ by 0.693, where λ is the decay/disintegration constant and the half-life is represented by t1/2. Mathematically Half-Life Formula is given by:
t1/2 = λ/0.693
Derivation of Formula of Half-Life
Let N be the concentration of the radioactive element at any given time t. If the decrease in the concentration of radioactive elements is dN in time interval dt, then the rate of radioactive decay is given by
dN/dt = -λt
[ where λ is the decay constant and the “-” sign represents the decrease in the concentration]
Integrating the above equation, we get
Example: A sample of radioactive material has a half-life of 10 days. If the initial mass of the sample is 100 grams, how much of it will remain after 30 days?
Solution:
λ = ln(2)/t1/2
where ln(2) is the natural logarithm of 2, and t1/2 is the half-life of the radioactive material.
Given t1/2 =10 days
So, λ = ln(2)/t1/2
⇒ λ = ln(2)/10
⇒ λ = ln(21/10)⇒ Nt = N0 e-λt
Nt = 100 x (1/2)3
Nt = 12.5
Thus, sample will reamain 12.5 gm after 30 days.
Radioactive Elements in Periodic Table
Radioactive Elements are the elements that emit radioactive waves like alpha waves, beta waves, and gamma waves. The Process is called Radioactivity. They are found throughout the Earth’s crust and have important applications in various fields, including medicines, energy production, etc. The radioactive elements are unstable because of the presence of excess nuclear charge inside their atomic nucleus. These atomic nuclei undergo radioactive decay to form stable nuclei. The elements that undergo radioactive decay are called radioactive elements.
Learn about, Types of Radioactivity
In this article, we will learn about radioactive elements, radioactive elements table, characteristics, examples, and applications of radioactive elements.
Table of Content
- What are Radioactive Elements?
- History of Radioactive Elements
- List of Natural Radioactive Elements
- What is Alpha Radiation?
- List of Radioactive Elements on the Periodic Table
- Examples of Radioactive Elements
- Radioactive Metals
- Radioactive Element Decay
- Half-Life
- Characteristics of Radioactive Elements
- Effects of Radioactive Elements
- Toxicity of Radioactive Elements
- Uses of Radioactive Elements