Question

A radioactive substance has a continuous decay rate of 0.056 per minute. How many grams of a 120 gram sample will remain radioactive after 40 minutes? Round the answer to the nearest tenth of a gram, and do not include the unit in your answer.

Answer 1

The mass of the radioactive sample after 40 minutes is 12.8 g.

Explanation:

The mass of the sample can be found by using the exponential decay equation:

`N_(t) = N_(0)e^(-\lambda t)`

Where:

N(t): is the amount of the sample at time t =?

N₀: is the initial quantity of the sample = 120 g

t = 40 min

λ: is the decay constant = 0.056 min⁻¹

Hence, the mass of the sample after 40 min is:

`N_(t) = N_(0)e^(-\lambda t) = 120g*e^{-0.056min^(-1)*40 min} = 12.8 g`

Therefore, the mass of the radioactive sample after 40 minutes is 12.8 g.

I hope it helps you!