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Chapter 43: Problem 13

What nuclide is produced in the following radioactive decays? (a) \(\alpha\) decay of \({ }_{94}^{239} \mathrm{Pu} ;\) (b) \(\beta\) decay of \({ }_{11}^{24} \mathrm{Na} ;\) (c) \(\beta^{+}\) decay of \({ }_{8}^{15} \mathrm{O}\).

Short Answer

Expert verified
The nuclides produced in the respective decays are: (a) \({ }_{92}^{235} \mathrm{U}\) (b) \({ }_{12}^{24} \mathrm{Mg}\) (c) \({ }_{7}^{15} \mathrm{N}\).

Step by step solution

01

- Alpha Decay of Pu-239

In an alpha decay, a nucleus emits an alpha particle, which consists of 2 protons and 2 neutrons. Thus for an \(\alpha\) decay of \({ }_{94}^{239} \mathrm{Pu}\), we subtract 2 from the atomic number and 4 from the atomic mass number to obtain the new nuclide. This gives us \({ }_{92}^{235} \mathrm{U}\).
02

- Beta Decay of Na-24

In a beta decay, a neutron is converted into a proton and an electron, which is then emitted. Thus for a \(\beta\) decay of \({ }_{11}^{24} \mathrm{Na}\), we add 1 to the atomic number while the atomic mass number remains unchanged. This gives us \({ }_{12}^{24} \mathrm{Mg}\).
03

- Positron Decay of O-15

In a positron decay, a proton is converted into a neutron and the released positron is then immediately emitted. So for a \(\beta^{+}\) decay of \({ }_{8}^{15} \mathrm{O}\), we subtract 1 from the atomic number and the atomic mass number remains unchanged. This gives us \({ }_{7}^{15} \mathrm{N}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Alpha Decay
In alpha decay, a radioactive nucleus emits an alpha particle. Alpha particles are composed of two protons and two neutrons. This means when an alpha particle is emitted, the original atom loses two protons and two neutrons.

Consequently, for each alpha decay:
  • The atomic number of the nuclide decreases by 2.
  • The mass number (sum of protons and neutrons) decreases by 4.
This change transforms the original element into a completely different element within the periodic table. For instance, in the alpha decay of plutonium-239 (\({ }^{239}_{94}\text{Pu}\)), the loss of 2 protons and 4 total nucleons results in uranium-235 (\({ }^{235}_{92}\text{U}\)). This process is a common form of decay for heavy elements and is often accompanied by the emission of energy in the form of radiation.
Beta Decay
During beta decay, a neutron in a nucleus transforms into a proton and emits an electron in the process. This emitted electron is known as a beta particle. As a result:
  • The atomic number increases by 1 since the newly formed proton is added to the atomic structure.
  • The mass number remains unchanged because the total number of nucleons (protons and neutrons) does not change.
For example, when sodium-24 (\({ }^{24}_{11}\text{Na}\)) undergoes beta decay, it transforms into magnesium-24 (\({ }^{24}_{12}\text{Mg}\)) because a neutron has turned into a proton, increasing the atomic number by 1.

Beta decay is a common decay mode for unstable isotopes with an excess of neutrons and results in the formation of new elements.
Positron Emission
Positron emission occurs when a proton in a radioactive nuclide transforms into a neutron, releasing a positron in the process. A positron is the antimatter counterpart of an electron. In this type of decay:
  • The atomic number decreases by 1, reflecting the change from proton to neutron.
  • The mass number remains unchanged, since there is no net loss of nucleons.
An example is oxygen-15 (\({ }^{15}_{8}\text{O}\)), which through positron emission changes into nitrogen-15 (\({ }^{15}_{7}\text{N}\)) as it converts a proton to a neutron, reducing the atomic number by 1.

Positron emission is part of a subclass of beta decay and occurs in isotopes where there is an excess of protons, balancing the internal nuclear forces.

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Most popular questions from this chapter

Measurements on a certain isotope tell you that the decay rate decreases from 8318 decays/min to 3091 decays/min in 4.00 days. What is the half-life of this isotope?

Thorium \({ }_{90}^{230} \mathrm{Th}\) decays to radium \({ }_{88}^{226} \mathrm{Ra}\) by \(\alpha\) emission. The masses of the neutral atoms are 230.033134 u for \({ }_{90}^{230} \mathrm{Th}\) and \(226.025410 \mathrm{u}\) for \({ }_{88}^{226} \mathrm{Ra}\). If the parent thorium nucleus is at rest, what is the kinetic energy of the emitted \(\alpha\) particle? (Be sure to account for the recoil of the daughter nucleus.)

Comparison of Energy Released per Gram of Fuel. (a) When gasoline is burned, it releases \(1.3 \times 10^{8} \mathrm{~J}\) of energy per gallon \((3.788 \mathrm{~L}) .\) Given that the density of gasoline is \(737 \mathrm{~kg} / \mathrm{m}^{3},\) express the quantity of energy released in \(\mathrm{J} / \mathrm{g}\) of fuel. (b) During fission, when a neutron is absorbed by a \({ }^{235} \mathrm{U}\) nucleus, about \(200 \mathrm{MeV}\) of energy is released for each nucleus that undergoes fission. Express this quantity in \(\mathrm{J} / \mathrm{g}\) of fuel. \((\mathrm{c})\) In the proton-proton chain that takes place in stars like our sun, the overall fusion reaction can be summarized as six protons fusing to form one \({ }^{4}\) He nucleus with two leftover protons and the liberation of \(26.7 \mathrm{MeV}\) of energy. The fuel is the six protons. Express the energy produced here in units of \(\mathrm{J} / \mathrm{g}\) of fuel. Notice the huge difference between the two forms of nuclear energy, on the one hand, and the chemical energy from gasoline, on the other. (d) Our sun produces energy at a measured rate of \(3.86 \times 10^{26} \mathrm{~W}\). If its mass of \(1.99 \times 10^{30} \mathrm{~kg}\) were all gasoline, how long could it last before consuming all its fuel? (Historical note: Before the discovery of nuclear fusion and the vast amounts of energy it releases, scientists were confused. They knew that the earth was at least many millions of years old, but could not explain how the sun could survive that long if its energy came from chemical burning.)

An alpha particle is strongly bound. The \({ }_{6}^{12} \mathrm{C}\) nucleus might be modeled as a composite of three alpha particles. Compare the binding energy of \({ }_{6}^{12} \mathrm{C}\) with three times the binding energy of an alpha particle. Which of these quantities is larger, and why might this be so?

As a health physicist, you are being consulted about a spill in a radiochemistry lab. The isotope spilled was \(400 \mu \mathrm{Ci}\) of \({ }^{131} \mathrm{Ba},\) which has a half-life of 12 days. (a) What mass of \({ }^{131}\) Ba was spilled? (b) Your recommendation is to clear the lab until the radiation level has fallen \(1.00 \mu \mathrm{Ci} .\) How long will the lab have to be closed?
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