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Chapter 42: Q 23 Exercise (page 1236)

The half-life of 60Co is 5.27 years. The activity of a 60Co

sample is 3.50 x 109 Bq. What is the mass of the sample?

Short Answer

Expert verified

Hence the mass of the sample is :8.361×10-8kg

Step by step solution

01

Given information

t1/2=5.27yearsR=3.50×109Bq

02

Explanation

We will use the formula:

R=r·N→(Equation 1.)

First, we must determine the value of the decay rate r:

r=1τr=ln(2)t1/2r=0.6935.27×3.15×107sr=0.6931.663×108sr=4.17×10-9s

Next, we must determine the value of N using equation 1:

R=r·NN=RrN=3.50×109decays/s4.17×10-9sN=8.39×1017atoms

03

Explanation

Finally, we will find the mass:

M=m·NM=60×1.661×10-27kg×8.39×1017M=8.361×10-8kg

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Most popular questions from this chapter

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.

Use the graph of binding energy to estimate the total energy released if three 4 He nuclei fuse together to form a 12 C nucleus

Identify the unknown isotope X in the following decays.

a.X→Ra224+αb.S35→X+e-+ν¯c.X→K40+e++νd.Na24→Mg24+e-+ν¯→X+γ

a. Draw energy-level diagrams, similar to Figure 42.11, for all A=14nuclei listed in Appendix C. Show all the occupied neutron and proton levels.

b. Which of these nuclei is stable? What is the decay mode of any that are radioactive?

a. What are the isotopic symbols of all A = 17 isobars?

b. Which of these are stable nuclei?

c. For those that are not stable, identify both the decay mode and the daughter nucleus.
See all solutions

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