If the half life of a particle is 4.5 how long will it decay 3/4 of its mass.

Question: If the half life of a particle is 4.5 how long will it decay 3/4 of its mass.

One of the most important concepts in nuclear physics is the half-life of a radioactive particle. The half-life is the time it takes for half of the particles in a sample to decay into another form. For example, if the half-life of a particle is 4.5 seconds, then after 4.5 seconds, half of the particles will have decayed and the other half will remain unchanged.

But what if we want to know how long it takes for a different fraction of the particles to decay, such as 3/4 or 1/4? In this blog post, we will show you how to calculate this using a simple formula.

The formula is based on the fact that the decay process is exponential, meaning that the rate of decay depends on how many particles are left. The more particles there are, the faster they decay. The formula is:

t = (ln(f) / ln(0.5)) * T

where t is the time it takes for a fraction f of the particles to decay, T is the half-life of the particle, and ln is the natural logarithm function.

Let's apply this formula to our example. If the half-life of a particle is 4.5 seconds, and we want to know how long it takes for 3/4 of the particles to decay, we plug in the values:

t = (ln(0.25) / ln(0.5)) * 4.5

t = (-1.386 / -0.693) * 4.5

t = 9 seconds

So it takes 9 seconds for 3/4 of the particles to decay. If we want to know how long it takes for 1/4 of the particles to decay, we can use the same formula with a different fraction:

t = (ln(0.75) / ln(0.5)) * 4.5

t = (-0.288 / -0.693) * 4.5

t = 1.87 seconds

So it takes 1.87 seconds for 1/4 of the particles to decay.

We hope this blog post has helped you understand how to calculate the time it takes for a fraction of radioactive particles to decay using the half-life concept. If you have any questions or comments, please leave them below.

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