Question

Barium-131 is a radioactive isotope of the element barium used for gastrointestinal tract scans in doctors offices. Barium-131 has a half-life of 10 days. If a patient drinks 2 grams of barium-131 how much of the isotope will be left after 10 days?

Answer 1

Answer:

The answer is 1 [gram]

Explanation:

The half-life of a radioactive substance is the time it takes the substance to decay to half of its original value. In other words, if I have 100grams of a substance whose half-life is 10days, then after 10-days I will only have 50grams.

The problem is simple enough because they want to know the amount of material in 10 days, and we know the definition of half-life and we know that the half-life of Barium-131 is 10 days, therefore the amount of Barium-131 left in 10 days will be half of the original mass of 2 [grams]

• 1 [gram]

Further explanation with real decay equations:

The decay equation for radioactive materials is:

• $N(t) = N_{0} e^{-kt}$

Where:

• N(t) is the value of the substance after "t" days
• N0 is the initial value of the substance
• k is the decay constant of the radioactive substance
• t is the period in days

To calculate the decay constant we use the following formula:

• $k = \frac{ln (2)}{half.life}$

And we know the half life is 10 days, so the constant is:

• k = .069314718

Substitute the decay constant k, t=10, N0 = 2 and find N(t) in equation 1:

• N(t) = 1 [gram]

Answer 2

1 gram of the barium 131 would be left after 10 days. since the half life is 10 days, you would divide the 2 grams by 2, leaving you with 1 gram.