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Suppose the half life of an isotope is 30 seconds and you have 10 grams to start with how much will you have after one minute

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Hello!

The half-life is the time of half-disintegration, it is the time in which half of the atoms of an isotope disintegrate.

We have the following data:

mo (initial mass) = 10 g

m (final mass after time T) = ? (in g)

x (number of periods elapsed) = ?

P (Half-life) = 30 seconds

T (Elapsed time for sample reduction) = 1 minute → 60 seconds

Let's find the number of periods elapsed (x), let us see:


T = x*P


60 = x*30


60 = 30\:x


30\:x = 60


x = (60)/(30)


\boxed{x = 2}

Now, let's find the final mass (m) of this isotope after the elapsed time, let's see:


m = (m_o)/(2^x)


m = (10)/(2^(2))


m = (10)/(4)


\boxed{\boxed{m = 2.5\:g}}\end{array}}\qquad\checkmark

I Hope this helps, greetings ... DexteR! =)

User James Mudd
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