Ask Me Help Desk - Half-life equation

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Half-life equation

Radium-226 has a half life of 1660 years.How many years does it take a radium sample to decay to 55% of the original amount. Round to the nearest year.
Please help me set up this equation!

here are some links:

Effective half-life - Wikipedia, the free encyclopedia

Radioactive decay - Wikipedia, the free encyclopedia

The equation you want is

$N = N_0 \,\times\, 2^{ \left( \frac {t}{t_{\frac 12} \right)$ (equation 1)

where $N_0$ is the original amount of material present. $t$ is the time in the same units as the half-life, $t_{ \frac 12 }$ is the half-life.

in your case $\frac {N}{N_0} = 0.55$

Divide both sides of equation 1 by $N_0$ . Enter the data you have and solve for t.

I got a negative answer... I I got it, you missed a 'minus' sign in front of your power of two Perito...

What's happening to you today? Tired?

We can easily find k, the constant of proportionately, from the formula for half-life:

$T=\frac{-1}{k}ln(2)$

Since we are given the half-life is 1660, all we need to do is solve for k.

$1660=-\frac{1}{k}ln(2)\Rightarrow \frac{-ln(2)}{1660}\approx -.00041756$

Now we can sub this into the equation and solve for t:

$.55A=Ae^{\frac{-ln(2)}{1660}t}$

Solve for t.

Can u put this in simple terms for me

Quote:

Originally Posted by bjones2379

can u put this in simple terms for me

What do you mean? You want to know how to find the answer to this question on half life? :confused:

Or do you perhaps have another question?

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