Chapter 19: Problem 35
What is the difference between radioactive decay and nuclear transmutation?
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Chapter 19: Problem 35
What is the difference between radioactive decay and nuclear transmutation?
These are the key concepts you need to understand to accurately answer the question.
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State the general rules for predicting nuclear stability.
The radioactive isotope \({ }^{238} \mathrm{Pu},\) used in pacemakers, decays by emitting an alpha particle with a half-life of 86 yr. (a) Write an equation for the decay process. (b) The energy of the emitted alpha particle is \(9.0 \times 10^{-13} \mathrm{~J},\) which is the energy per decay. Assuming that all the alpha particle energy is used to run the pacemaker, calculate the power output at \(t=0\) and \(t=10 \mathrm{yr} .\) Initially \(1.0 \mathrm{mg}\) of \({ }^{238} \mathrm{Pu}\) was present in the pacemaker. (Hint: After \(10 \mathrm{yr}\), the activity of the isotope decreases by 8.0 percent. Power is measured in watts or \(\mathrm{J} / \mathrm{s}\).
In the chapter, we learned to calculate the nuclear binding energy, which pertains to the stability of a particular nucleus. It is also possible to estimate the binding energy of a single nucleon (neutron or proton) to the remainder of the nucleus. (a) From the following nuclear equation and nuclear masses, calculate the binding energy of a single neutron: $${ }_{7}^{14} \mathrm{~N} \longrightarrow{ }_{7}^{13} \mathrm{~N}+{ }_{0}^{1} \mathrm{n}$$ (Useful information: \({ }_{7}^{14} \mathrm{~N}: 14.003074 \mathrm{amu} ;{ }_{7}^{13} \mathrm{~N}:\) 13.005738 amu; \({ }_{0}^{1} \mathrm{n}: 1.00866\) amu. \()\) (b) By a similar procedure, we can calculate the binding energy of a single proton according to the equation $${ }_{7}^{14} \mathrm{~N} \longrightarrow{ }_{6}^{13} \mathrm{C}+{ }_{1}^{1} \mathrm{p}$$ (Useful information: \({ }_{6}^{13} \mathrm{C}: 13.003355 \mathrm{amu} ;{ }_{1}^{1} \mathrm{p}:\) 1.00794 amu.) Comment on your results.
(a) Calculate the energy released when an U-238 isotope decays to Th-234. The atomic masses are \(\begin{array}{llll}\text { given by } & \text { U-238: } & 238.0508 & \text { amu; } & \text { Th-234: }\end{array}\) 234.0436 amu; He-4: 4.0026 amu. (b) The energy released in (a) is transformed into the kinetic energy of the recoiling Th- 234 nucleus and the \(\alpha\) particle. Which of the two will move away faster? Explain.
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