Question

1.      Radon 222 is released from the earth and can become trapped in buildings. Suppose the concentration measured in a college classroom building is 1500 pCi/m³, which is significantly above the recommended remedial action level of 4 to 8 pCi/m³ if all leaks into the building are sealed (i.e., no more radon enters the building), how long will it take for the concentration of radon to reach the recommended level?

Answer 1

Answer-1)

Given:

The Radon 222 concentration in college classroom building = 1500 pCi/m³.

The recommended remedial action level of Radon 222 = [4-8 pCi/m³ ].

To calculate: The time it will take for the concentration of radon 222 to reach the recommended level.

Solve:

(i) To calculate The time it will take for the concentration of radon 222 to reach the recommended level in the building we will use the following radioactive law relation-

A₁ = A₀ x e^(-λt).

Where A₁ is the Activity (no. of radioactive deacy substance undergoes per second ) of radioactive substance after time t, A₀ is the activity of the radioactive substance at time t = 0, and λ is the decay constant.

And the decay constant can be calculated using the following relation-

λ = ln(2) / t_1/2 = 0.693 / t_1/2.

Where t_1/2 is the half-life of the radioactive substance.

Now We know that the halflife of radon 222 = 3.8 days so the decay constant for radon 222 gas is -

λ = 0.693 / t_1/2.

λ = 0.693 / 3.8

λ = 0.1824 days^-1.

(ii) So the initial activity (i.e at t= 0) of the radon 222 gas is 1500 pCi/m³, and let after time 't' the activity of the radon 222 gas is 8 pCi/m³ (taking upper limit of the recommended remedial action level of Radon 222 ), Then using the radioactive law relation-

A₁ = A₀ x e^(-λt).

Substituting the values of λ , A₁ and A₀ in the above relation we get-

8 pCi/m³ = 1500 pCi/m³ x e^{(-0.1824 days-1 x t)}.

0.00533 = e^{(-0.1824 days-1 x t)}.

taking natural log both the side we get-

-5.23378 = -0.1824 days^-1x t

t = 28.7 days

Similarly if we take the lower limit of the recommended remedial action level of Radon 222 (i.e 4 pCi/m³ ), we get-

4 pCi/m³ = 1500 pCi/m³ x e^{(-0.1824 days-1 x t)}.

0.00266 = e^{(-0.1824 days-1 x t)}.

taking natural log both the side we get-

-5.927 = -0.1824 days^-1x t

t = 32.5 days

Answer: So The time it will take for the concentration of radon 222 to reach the recommended level is between 28.7 days to 32.5 days.

Hope you understood the answer.

Best Wishes!