Because of the 1986 explosion and fire in a reactor at the...

Because of the 1986 explosion and fire in a reactor at the Chernobyl nuclear power plant in northern Ukraine, part of Ukraine is contaminated with 137 $\mathrm{Cs}$ , which undergoes beta-minus decay with a half-life of 30.2 $\mathrm{y}$ . In $1996,$ the total activity of this con- tamination over an area of $2.6 \times 10^{5} \mathrm{km}^{5}$ was estimated to be 1 $\mathrm{x}$ $10^{16} \mathrm{Bq} .$ Assume that the 13 $\mathrm{Cs}$ is uniformly spread over that area and that the beta-decay electrons travel either directly upward or directly downward. How many beta-decay electrons would you in- tercept were you to lie on the ground in that area for 1 $\mathrm{h}$ (a) in 1996 and (b) today? (You need to estimate your cross-sectional area that intercepts those electrons.)

Because of the 1986 explosion and fire in a reactor at the
Chernobyl nuclear power plant in northern Ukraine, part of
Ukraine is contaminated with 137 $\mathrm{Cs}$ , which undergoes beta-minus
decay with a half-life of 30.2 $\mathrm{y}$ . In $1996,$ the total activity of this con-
tamination over an area of $2.6 \times 10^{5} \mathrm{km}^{5}$ was estimated to be 1 $\mathrm{x}$
$10^{16} \mathrm{Bq} .$ Assume that the 13 $\mathrm{Cs}$ is uniformly spread over that area
and that the beta-decay electrons travel either directly upward or
directly downward. How many beta-decay electrons would you in-
tercept were you to lie on the ground in that area for 1 $\mathrm{h}$ (a) in 1996
and (b) today? (You need to estimate your cross-sectional area
that intercepts those electrons.)

Key Concepts

Cross-sectional Area

Cross-sectional area refers to the effective area over which radiation, such as beta particles, is intercepted by an object or a person. Estimating this area is crucial in calculating the number of emitted decay particles that actually interact with a target.

Exponential Decay

Exponential decay describes the mathematical relationship governing the decrease in the number of radioactive nuclei over time. It uses the concept of half-life to compute future activity levels, showing that the quantity decreases by a constant factor in equal time intervals.

Beta Decay

Beta decay is a type of radioactive decay in which a beta particle, typically an electron, is emitted from an atomic nucleus. Understanding this process is essential for assessing radiation exposure as beta particles contribute to the radiation dose received.

Half-life

Half-life is the time required for half of the radioactive nuclei in a sample to decay. It is a key parameter in describing exponential decay processes and is used to determine how the radioactivity of a substance decreases over time.

Radioactive Decay

This refers to the natural process by which an unstable atomic nucleus loses energy by emitting radiation. The concept encompasses the idea that the probability of decay is constant over time, leading to a predictable rate of decay characterized by parameters such as half-life and activity.

Activity (Becquerels)

Activity is a measure of the rate of radioactive decay, expressed in becquerels (Bq), where one becquerel corresponds to one decay event per second. It indicates how many radioactive disintegrations occur in a sample per unit time.

Transcript

00:01 Problem 42 .80, we're thinking about the beta radiation from the cesium 137 that contaminates a large part of the ukraine from the chernobyl incident in 1986.

00:20 So we're told what the half -life is of this beta decay of cesium.

00:25 And we're told that in 1996, there were 10 to the 16th becquerels spread over 2 .6 times 10 to the 5th square kilometers.

00:34 And so we want to imagine laying on the ground for one hour and figuring out the number of electrons that our body intercepts, both in 1996 and today, which as of this recording, is 2019.

00:48 But since we're going to, you know, go through the sort of actual work to get to the number for 2019, you can figure it out for any year you like.

01:04 So, first of all, we have to make an assumption about the sort of projected area of your body, which we're just going to assume is one square meter.

01:23 Again, you can use whatever number you like for this, but this is the easiest and it's probably fairly close.

01:33 We're also told to assume that half of the betas go straight up and half go straight down into the ground.

01:39 That's important.

01:43 And then none go in any other directions.

01:55 So the rate, wait, rate.

02:08 So the rate of beta is going through you divided by the total rate we're given is just equal to the ratio of the areas.

02:23 So a sub y for you...