Question

Explosions at a disabled nuclear power station in Japan, in 2011 may have released more cesium-137 (t1/2 = 30.2 years) into the ocean than any other single event. How long will the radioactivity of this radionuclide take to decay to 6.00% of the level released in 2011?

Answer 1

It will take approximately 161 years for the radioactivity of cesium-137 to decay to 6.00% of the original level released in the 2011 explosion at a nuclear power station in Japan.

Step-by-step explanation:

The question is concerned with the decay of the radioactive isotope cesium-137 (Cs-137) to 6.00% of its original activity following the disabled nuclear power station explosion in Japan in 2011. Cesium-137 has a half-life of 30.2 years. To calculate how long it will take for the radioactivity to decay to 6.00% of the initial level, we use the formula for exponential decay based on the half-life:

A(t) = A_0 · (1/2)^(t/t1/2)

Where:

• A(t) is the activity at time t.
• A_0 is the initial activity.
• t is the time elapsed.
• t1/2 is the half-life of the isotope.

We want to find the time t when A(t)/A_0 = 6.00/100 = 0.06.

Rearranging the decay formula and solving for t gives:

0.06 = (1/2)^(t/30.2)
Solving for t gives:

t = -30.2 · log2(0.06) ≈ 161 years

So, it will take approximately 161 years for the radioactivity of Cs-137 to decay to 6.00% of its original level after the event in 2011.