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Q. 59

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 1238

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Short Answer

The uranium isotope is naturally present at low levels in many soils. One of the nuclei in the decay series of is the radon isotope , which decays by emitting a alpha particle with days. Radon is a gas, and it tends to seep from soil into basements. The Environmental Protection Agency recommends that homeowners take steps to remove radon, by pumping in fresh air, if the radon activity exceeds of air.

a. How many atoms are there in of air if the activity is ?

b. The range of alpha particles in air is . Suppose we model a person as a -tall, -diameter cylinder with a mass of . Only decays within of the cylinder can cause exposure, and only , of the decays direct the alpha particle toward the person. Determine the dose in for a person who spends the entire year in a room where the activity is .

c. Does the EPA recommendation seem appropriate? Why?

(a) No. of atoms are,

(b) Dose is,

(c) This dose is roughly of the natural background of radioactivity.

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Step by Step Solution

Part (a) Step 1: Given information

We are given that,

Half life of alpha particle is,

Activity is,

Part (a) Step 2: Simplify

We know that,

Decay rate is given as,

Now, activity for in

Therefore, No. of atoms are,

Part (b) Step 1: Given information

We are given that,

Height of model of person is,

Diameter of model of person is,

Mass is,

Part (b) Step 2: Simplify

As diameter is given so radius is,

Volume of air is,

Here, is radius of cylinder

And is height of cylinder

No. of decays per second is,

No. of alpha particles is,

Dose is,

Part (c) Step 1: Given information

We need to find out that,

EPA recommendation is appropriate or not

Part (c) Step 2: Explanation

The dose is roughly of the natural background of radioactivity. This is due to EPA standards which is set to be .

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