Chapter 42: Q 25 Exercise (page 1236)
Identify the unknown isotope X in the following decays.
Short Answer
Hence, the values of X are:
/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none}
Learning Materials
Features
Discover
Chapter 42: Q 25 Exercise (page 1236)
Identify the unknown isotope X in the following decays.
Hence, the values of X are:
All the tools & learning materials you need for study success - in one app.
Get started for free
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?
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?
Alpha decay occurs when an alpha particle tunnels through the Coulomb barrier. FIGURE CP42.63 shows a simple one-dimensional model of the potential-energy well of an alpha particle in a nucleus with A ≈ 235. The 15 fm width of this one-dimensional potential-energy well is the diameter of the nucleus. Further, to keep the model simple, the Coulomb barrier has been modeled as a 20-fm-wide, 30-MeV-high rectangular potential-energy barrier. The goal of this problem is to calculate the half-life of an alpha particle in the energy level E = 5.0 MeV. a. What is the kinetic energy of the alpha particle while inside the nucleus? What is its kinetic energy after it escapes from the nucleus? b. Consider the alpha particle within the nucleus to be a point particle bouncing back and forth with the kinetic energy you found in part a. What is the particle’s collision rate, the number of times per second it collides with a wall of the potential? c. What is the tunneling probability Ptunnel ? d. Ptunnel is the probability that on any one collision with a wall the alpha particle tunnels through instead of reflecting. The probability of not tunneling is 1 - Ptunnel. Hence the probability that the alpha particle is still inside the nucleus after N collisions is 11 - Ptunnel 2N ≈ 1 - NPtunnel , where we’ve used the binomial approximation because Ptunnel V 1. The half-life is the time at which half the nuclei have not yet decayed. Use this to determine (in years) the half-life of the nucleus.

A 115 mCi radioactive tracer is made in a nuclear reactor. When it is delivered to a hospital 16 hours later its activity is 95 mCi. The lowest usable level of activity is 10 mCi.
a. What is the tracer’s half-life?
b. For how long after delivery is the sample usable?
What is the total energy (in MeV) released in the beta decay
of a neutron?
What do you think about this solution?
We value your feedback to improve our textbook solutions.