Question

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

Answer 1

Hello!

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

• We have the following data:

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

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:

$T = x*P$

$8 = 2*P$  

$2\:P = 8$

$P = \dfrac{8}{2}$

$\boxed{\boxed{P = 4\:minutes}}\Longleftarrow(Half-Life)\:\:\:\:\:\:\bf\green{\checkmark}$

Answer:

The half-life is 4 minutes

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