Question

Suppose that 0.50 grams of barium-131 are administered orally to a patient. Approximately how many milligrams of the barium would still be radioactive two months later?

Answer 1

Two months later 13.8 milligrams of the barium-131 still be radioactive.

How is the decay rate of a radioactive substance expressed ?

It is expressed as:

$A = A_{0} \times (\frac{1}{2})^{t/T}$

where,

A = Amount remaining

A₀ = Initial Amount

t = time

T = Half life

Here

A₀ = 0.50g

t  = 2 months = 60 days

T = 11.6 days  

Now put the values in above expression we get

$A = A_{0} \times (\frac{1}{2})^{t/T}$

   $= 0.50 \times (\frac{1}{2})^{60/11.6}$

   $= 0.50 \times (\frac{1}{2})^{5.17}$

   = 0.50 × 0.0277

   = 0.0138 g

   = 13.8 mg          [1 mg = 1000 g]

Thus from the above conclusion we can say that Two months later 13.8 milligrams of the barium-131 still be radioactive.

Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: Suppose that 0.50 grams of ban that 0.50 grams of barium-131 are administered orally to a patient. Approximately many milligrams of the barium would still be radioactive two months later? The half-life of barium-131 is 11.6 days.

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