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Chapter 19: Problem 63

Write complete nuclear equations for the following processes: (a) tritium, \({ }^{3} \mathrm{H},\) undergoes \(\beta\) decay; (b) \({ }^{242}\) Pu undergoes \(\alpha\) -particle emission; (c) \({ }^{131} \mathrm{I}\) undergoes \(\beta\) decay; (d) \({ }^{251} \mathrm{Cf}\) emits an \(\alpha\) particle.

Short Answer

Expert verified
The nuclear equations for the processes are: (a) \({ }^{3}\mathrm{H}\) \(\rightarrow\) \({ }^{3}\mathrm{He}\) + \(e^{-}\), (b) \({ }^{242}\mathrm{Pu}\) \(\rightarrow\) \({ }^{238}\mathrm{U}\) + \({ }^{4}\mathrm{He}\), (c) \({ }^{131} \mathrm{I}\) \(\rightarrow\) \({ }^{131} \mathrm{Xe}\) + \(e^{-}\), (d) \({ }^{251}\mathrm{Cf}\) \(\rightarrow\) \({ }^{247}\mathrm{Cm}\) + \({ }^{4}\mathrm{He}\).

Step by step solution

01

Understand the Processes

The nature of the processes involved in a nuclear reaction are important to understand. In beta decay, a neutron is converted into a proton and an electron, which is released as a beta particle. In alpha emission, the nucleus releases an alpha particle, which is a helium nucleus, reducing the atomic number by 2 and mass number by 4.
02

Nuclear Equation for Beta Decay of Tritium

In beta decay, a neutron is converted into a proton and a beta particle. The atomic number increases by 1 while the mass number remains same. So, the equation for beta decay of Tritium \({ }^{3}\mathrm{H}\) is: \({ }^{3}\mathrm{H}\) \(\rightarrow\) \({ }^{3}\mathrm{He}\) + \(e^{-}\)
03

Nuclear Equation for Alpha Particle Emission of Pu

In alpha particle emission, the nucleus releases an alpha particle (helium nucleus) thereby reducing atomic number by 2 and mass number by 4. So, the equation for alpha particle emission of \({ }^{242}\) Pu is: \({ }^{242}\mathrm{Pu}\) \(\rightarrow\) \({ }^{238}\mathrm{U}\) + \({ }^{4}\mathrm{He}\)
04

Nuclear Equation for Beta Decay of I

The beta decay of \({ }^{131} \mathrm{I}\) results in the conversion of a neutron to a proton and a beta particle, thereby increasing atomic number by 1 and keeping the mass number the same. Therefore, the nuclear equation for beta decay of \({ }^{131} \mathrm{I}\) is: \({ }^{131} \mathrm{I}\) \(\rightarrow\) \({ }^{131} \mathrm{Xe}\) + \(e^{-}\)
05

Nuclear Equation for Alpha Particle Emission of Cf

The alpha particle emission of \({ }^{251}\mathrm{Cf}\) involves the release of an alpha particle (helium nucleus), which leads to a decrease in atomic number by 2 and mass number by 4. Therefore, the nuclear equation for alpha particle emission of \({ }^{251}\mathrm{Cf}\) is: \({ }^{251}\mathrm{Cf}\) \(\rightarrow\) \({ }^{247}\mathrm{Cm}\) + \({ }^{4}\mathrm{He}\)

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Most popular questions from this chapter

As a result of being exposed to the radiation released during the Chernobyl nuclear accident, the dose of iodine-131 in a person's body is \(7.4 \mathrm{mCi}\) \(\left(1 \mathrm{mCi}=1 \times 10^{-3} \mathrm{Ci}\right) .\) Use the relationship rate \(=\lambda N\) to calculate the number of atoms of iodine- 131 to which this radioactivity corresponds. (The halflife of \({ }^{131} \mathrm{I}\) is 8.1 d. \()\).

Nuclei with an even number of protons and an even number of neutrons are more stable than those with an odd number of protons and/or an odd number of neutrons. What is the significance of the even numbers of protons and neutrons in this case?

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 \(\mathrm{J} / \mathrm{s}\).

Calculate the energy released (in joules) from the following fusion reaction: $${ }_{1}^{2} \mathrm{H}+{ }_{1}^{3} \mathrm{H} \longrightarrow{ }_{2}^{4} \mathrm{He}+{ }_{0}^{1} \mathrm{n}$$ The atomic masses are \({ }_{1}^{2} \mathrm{H}=2.0140 \mathrm{amu},{ }_{1}^{3} \mathrm{H}=3.01603\) \(\mathrm{amu},{ }_{2}^{4} \mathrm{He}=4.00260 \mathrm{amu},{ }_{0}^{1} \mathrm{n}=1.008665 \mathrm{amu}\).

To detect bombs that may be smuggled onto airplanes, the Federal Aviation Administration (FAA) will soon require all major airports in the United States to install thermal neutron analyzers. The thermal neutron analyzer will bombard baggage with low-energy neutrons, converting some of the nitrogen- 14 nuclei to nitrogen- \(15,\) with simultaneous emission of \(\gamma\) rays. Because nitrogen content is usually high in explosives, detection of a high dosage of \(\gamma\) rays will suggest that a bomb may be present. (a) Write an equation for the nuclear process. (b) Compare this technique with the conventional X-ray detection method.
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