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Chapter 42: Q.48 (page 1237)
A 1 Ci source of radiation is a significant source. 238 U is an alpha emitter. What mass of 238 U has an activity of 1 Ci?
the mass of uranium is 2.96x103kg
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Nucleus A decays into nucleus B with a half-life of 10 s. At
t = 0 s, there are 1000 A nuclei and no B nuclei. At what time
will there be 750 B nuclei?
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 localid="1650487447445" alpha particle with localid="1650487458663" 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?
All the very heavy atoms found in the earth were created long ago by nuclear fusion reactions in a supernova, an exploding star. The debris spewed out by the supernova later coalesced into the gases from which the sun and the planets of our solar system were formed. Nuclear physics suggests that the uranium isotopes 235 U and 238 U should have been created in roughly equal numbers. Today, 99.28% of uranium is 238 U and only 0.72% is 235 U. How long ago did the supernova occur?
The technique known as potassium-argon dating is used to date old lava flows. The potassium isotope 40 K has a 1.28-billionyear half-life and is naturally present at very low levels. 40 K decays by two routes: 89% undergo beta-minus decay into 40 Ca while 11% undergo electron capture to become 40 Ar. Argon is a gas, and there is no argon in flowing lava because the gas escapes. Once the lava solidifies, any argon produced in the decay of 40 K is trapped inside and cannot escape. A geologist brings you a piece of solidified lava in which you find the 40 Ar/ 40 K ratio to be 0.013. What is the age of the rock?
A sample contains radioactive atoms of two types, A and B. Initially there are five times as many A atoms as there are B atoms. Two hours later, the numbers of the two atoms are equal. The half-life of A is . What is the half-life of B?
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