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Charra [1.4K]
3 years ago
5

What is the half-life of 20 g of a radioactive sample if 5 g remain after 8 minutes?

Chemistry
1 answer:
Anni [7]3 years ago
5 0

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) = 20 g

m (final mass after time T) = 5 g

x (number of periods elapsed) = ?

P (Half-life) = ? (in minutes)

T (Elapsed time for sample reduction) = 8 minutes

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

m =  \dfrac{m_o}{2^x}

5 =  \dfrac{20}{2^x}

2^x = \dfrac{20}{5}

2^x = 4

2^x = 2^2

\boxed{x = 2}


Now, let's find the half-life (P) of the radioactive sample, let's see:

T = x*P

8 = 2*P

2\:P = 8

P = \dfrac{8}{2}

\boxed{\boxed{P = 4\:minutes}}\Longleftarrow(Half-Life)\end{array}}\qquad\checkmark

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

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