Half-Life ✏ Chemistry In a Nutshell

Rucete ✏ Chemistry In a Nutshell

1. What is Half-Life?

• Half-life (t₁/₂) is the time required for half of a radioactive isotope to decay.
• Each isotope has a unique half-life, which can range from fractions of a second to millions of years.

 

 

2. Half-Life Formula

The decay of a radioactive substance follows an exponential decay model:

$$N = N_0 \times e^{-kt}$$

or in logarithmic form:

$$\ln \left(\frac{N}{N_0}\right) = -0.693 \times \frac{t}{t_{1/2}}$$

Where:

• N₀ = Initial amount of substance
• N = Amount remaining after time t
• t₁/₂ = Half-life
• k = Decay constant (related to the half-life)

 

 

3. Common Examples of Half-Lives

Isotope	Half-Life	Use
Carbon-14 (¹⁴C)	5,730 years	Radiocarbon dating
Uranium-238 (²³⁸U)	4.5 billion years	Geological dating
Iodine-131 (¹³¹I)	8 days	Medical treatments
Polonium-210 (²¹⁰Po)	138 days	Toxic radioactive material

 

 

In a nutshell

• Independent of external conditions (temperature, pressure, etc.).
• Each half-life, 50% of the remaining substance decays.
• Used to determine the age of objects (e.g., carbon dating, uranium dating).
• Shorter half-life = Faster decay and vice versa.