Approximately how long will it take a 100-gram sample of francium-223 to decay to 20 grams?

Answers

Answer 1

Answer: 50 minutes

Answer choices:

20 minutes

70 minutes

50 minutes

30 minutes

Answer 2

It will take 68.8 minutes for a 100-gram sample of francium-223 to decay to 20 grams.

What is an equation?

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

The decay of a radioactive substance can be modeled by the exponential decay formula:

[tex]N(t) = N_0 ~ e^{-ct}[/tex]

where:

N(t) is the amount of the substance at time t

N0 is the initial amount of the substance

c is the decay constant

t is the time elapsed since the initial measurement

The half-life of francium-223 is about 22 minutes.

t = 22

Now,

0.5 = [tex]e^{-c \times22}[/tex]

ln (0.5) = -c x 22

c = ln(2) / 22

c ≈ 0.03159

Now,

We can use the formula to solve for the time it takes for the sample to decay from 100 grams to 20 grams.

20 = 100 x [tex]e^{-0.03159t}[/tex]

[tex]e^{-0.03159t}[/tex] = 0.2

-0.03159 t = ln(0.2)

t = ln(0.2) / (-0.03159)

t = 68.8 minutes

Therefore,

It will take 68.8 minutes for a 100-gram sample of francium-223 to decay to 20 grams.

Learn more about equations here:

https://brainly.com/question/17194269

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