How to Calculate Half-Life: 8 Steps (with Pictures)

2024 Author: Jason Gerald | [email protected]. Last modified: 2024-01-19 22:11

The half-life of a compound's decay is the time it takes for it to shrink by half. Initially, half-life was used to describe the decay of radioactive elements such as uranium or plutonium, but it can be used for any compound that decays at an exponential rate. You can calculate the half-life of any compound, because the rate of decay is calculated from the initial amount of the compound and the amount that remains after a certain amount of time. See Step 1 for a quick way to calculate half-life.

Step

Method 1 of 2: Calculating Half-Time

Step 1. Divide the number of compounds at a point by the number that remains after a certain amount of time

• The half-life calculation formula is as follows: t_1/2 = t * ln(2)/ln(N₀/N_t)
• In the formula, t = time, N₀ = number of compounds at the starting point, and N_t = number of compounds after some time (t).
• For example, if the initial amount of the compound is 1500 grams, and the final amount is 1000 grams, then the initial amount divided by the final amount becomes 1.5. Let's say the time elapsed for the compound is (t) = 100 minutes.

Step 2. Calculate the logarithm (log) value of the sum in the previous step

All you need to do is type log(1, 5) into your calculator to get the result.

• The logarithmic value of a number with a certain base number is the exponent of which the base number will be raised to the power (or the number of products where the base number is multiplied by its own value) to produce the number. Common logarithms use a base of 10. The log button on your calculator is a general logarithm.
• When you find that log (1, 5) = 0.176, this means that the general log value of 1.5 is equal to 0.176. This means that 10 to the power of 0.176 equals 1.5.

Step 3. Multiply the elapsed time by the general log value of 2 and by the number of elapsed times

If using a calculator you find that log(2) is equal to 0, 30103. Remember that the time that the compound has passed is 100 minutes.

For example, if the time elapsed by the compound is 100 minutes, then multiply 100 by 0, 30103. The result is 30, 103

Step 4. Divide the number you calculated in step three by the number you calculated in step two

For example, 30, 103 divided by 0.176 equals 171, 04. This value is the half-life of the compound expressed in units of time used in the third step

Step 5. Done

Now that you've figured out the half-life for this problem, you should understand that you can also use ln (the natural logarithm) to replace the general logarithm, and get the same value. And in fact, natural logarithms are used more in calculating half-lives.

Thus, you may find ln of 1, 5 (0, 405) and ln of 2 (0, 693). Then, if you multiply ln 2 by 100 9time), to get 0.693 x 100, or 69, 3, and then divide that number by 0.405, you get the value 171, 04, which is the same answer if you Answer it using the general logarithm

Method 2 of 2: Solving Part-Time Problems

Step 1. Calculate how much of a compound with a known half-life will remain after a certain number of days

Solve the problem: If 20 mg of Iodine-131 is given to the patient, how much is left after 32 days? The half-life of Iodine-131 is 8 days. Here's what you need to do:

• Find how much the compound is divided by two in 32 days. Do this by determining what number when multiplied by 8 which is the half-life of the compound, you get 32. 32/8 = 4, so the sum of the compounds divided by two is four times.
• This means that after 8 days you will have 20mg/2, or 10 mg of compound, after 16 days it will be 10 mg/2 or 4 mg remaining, after 24 days it will be 5 mg/2, or 2.5 mg of compound remaining., and after 32 days, you will have 2.5 mg/2, or 1.25 mg of the compound remaining.

Step 2. Find the half-life of a compound with a known initial and final number, and times

Solve the problem: If a laboratory receives a delivery of 200 g of technetium-99m and only 12.5 g remains in 24 hours. So what is the half-life of technetium-99m? Here's what you need to do:

• Reverse count. If 12.5 g of the compound remains, then before it becomes half, there are 25 g (12.5 x 2); previously there was 50 g of the compound; Previously there was 100 gr, and previously there was 200 gr.
• This means that the compound must be halved four times to make 12.5 g from 200 g, which means that its half-life is 24 hours/4 times or 6 hours.

Step 3. Calculate the number of half-lives required to decay the compound to a certain amount

Solve this problem: If the half-life of uranium-232 is 70 years, how many times the half-life is needed to convert 20 grams of uranium-232 to 1.25 grams? Here's what you need to do:

Start with 20 g and start reducing it. 20 g/2 = 10 g (1 half-life), 10 g/2 = 5 (2 half-life), 5 g/2 = 2.5 (3 half-life), and 2.5/2 = 1.25 (4 half-life). The answer is 4 times the half-life