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.
We are given that,
Half life of alpha particle is,
We know that,
Decay rate is given as,
Now, activity for in
Therefore, No. of atoms are,
We are given that,
Height of model of person is,
Diameter of model of person is,
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,
We need to find out that,
EPA recommendation is appropriate or not
The dose is roughly of the natural background of radioactivity. This is due to EPA standards which is set to be .
Stars are powered by nuclear reactions that fuse hydrogen into helium. The fate of many stars, once most of the hydrogen is used up, is to collapse, under gravitational pull, into a neutron star. The force of gravity becomes so large that protons and electrons are fused into neutrons in the reaction . The entire star is then a tightly packed ball of neutrons with the density of nuclear matter.
a. Suppose the sun collapses into a neutron star. What will its radius be? Give your answer in .
b. The sun's rotation period is now 27 days. What will its rotation period be after it collapses?
Rapidly rotating neutron stars emit pulses of radio waves at the rotation frequency and are known as pulsars.
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