How to Calculate Half Life in Physics IGCSE
If you’re studying physics at the IGCSE level, you’ve likely come across the concept of half-life. Half-life is a crucial concept in nuclear physics and is used to determine the decay rate of radioactive substances. In this article, we’ll guide you through the steps necessary to calculate the half-life of a radioactive substance.
Understand the Concept of Half-Life
Before we dive into the calculations, it’s important to understand what half-life means. Half-life is the time it takes for half of the radioactive atoms in a substance to decay. This means that if you start with 100 radioactive atoms, after one half-life, you will have 50 radioactive atoms left.
Identify the Decay Constant
The decay constant, denoted by λ, is a constant that characterizes the rate at which the radioactive substance decays. It is given by the equation λ = ln(2)/t₁/₂, where ln(2) is the natural logarithm of 2 and t₁/₂ is the half-life of the substance.
Determine the Initial Activity
The initial activity, denoted by A₀, is the number of radioactive decays per unit time at the beginning of the experiment. It can be calculated from the following equation: A₀ = λN₀, where N₀ is the initial number of radioactive atoms.
Calculate the Final Activity
The final activity, denoted by A, is the number of radioactive decays per unit time at some time t. It can be calculated from the following equation: A = λNt, where Nt is the number of radioactive atoms at time t.
Find the Time Interval
The time interval, denoted by Δt, is the time between the initial and final measurements of the activity. It can be calculated by subtracting the start time from the end time.
Calculate the Half-Life
The half-life, denoted by t₁/₂, can be calculated using the following equation: t₁/₂ = ln(2)/λ. This equation relates the decay constant to the half-life of the substance.
Put It All Together
Now that we have all the necessary equations, we can put them together to calculate the half-life of the substance. First, we need to measure the initial activity and the final activity at some time t. Then, we can calculate the time interval between the two measurements. Finally, we can use the equations we derived earlier to calculate the half-life of the substance.
Let’s work through an example to solidify our understanding. Suppose we have a sample of radioactive material with an initial activity of 500 decays per second. After 10 seconds, we measure the activity to be 125 decays per second. What is the half-life of the substance?
First, let’s calculate the decay constant: λ = ln(2)/t₁/₂ = ln(2)/10 = 0.0693 s⁻¹.
Next, let’s calculate the final number of radioactive atoms: A = λNt = 0.0693 x 500 x 10 = 346.5 decays per second.
Now, let’s calculate the time interval: Δt = 10 - 0 = 10 seconds.
Finally, let’s use the equation for half-life to find t₁/₂: t₁/₂ = ln(2)/λ = ln(2)/0.0693 = 10 seconds. Therefore, the half-life of the substance is 10 seconds.
Practice, Practice, Practice
The best way to master the concept of half-life and its calculations is through practice. Try working through different examples until you feel confident in your understanding.