If there are 180 grams of radioactive material with a half-life (decrease by half or 50%) of 1 hour, how much of the radioactive material will be left after 3 hours?

Answers

Answer 1

Answer:

After 3 hours there is left 22.5 grams of radioactive material.

Step-by-step explanation:

We can calculate the mass of radioactive material remaining after 3 hours, by using the decay equation:           

[tex]N_{t} = N_{0}*e^{-\lambda t}[/tex]     (1)

Where:

[tex]N_{0}[/tex]: is the initial mass = 180 g

[tex]N_{t}[/tex]: is the remaining mass after time t

λ: is the decay constant

The decay constant is given by:

[tex] \lambda = \frac{ln(2)}{t_{1/2}} [/tex]

Where [tex]t_{1/2}[/tex] = 1 h.

By entering λ into equation (1) we hve:

[tex] N_{t} = N_{0}*e^{-\frac{ln(2)}{t_{1/2}} t} [/tex]

[tex] N_{t} = 180 g*e^{-\frac{ln(2)}{1 h} 3 h} = 22.5 g [/tex]

Therefore, after 3 hours there is left 22.5 grams of radioactive material.

I hope it helps you!          


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Step-by-step explanation:

Answer:

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