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Polonium- 216 decays to lead- 212 by emission of an alpha particle. Which of the following is the nuclear equation for this radioactive decay? a) \({ }^{216} \mathrm{Po} \longrightarrow{ }_{84}^{212} \mathrm{~Pb}+{ }_{-1}^{0} \mathrm{e}\) b \({ }_{84}^{216} \mathrm{Po} \longrightarrow{ }_{82}^{212} \mathrm{~Pb}+{ }_{2}^{4} \mathrm{He}\) c) \({ }_{84}^{216} \mathrm{Po}+{ }_{2}^{4} \mathrm{He} \longrightarrow{ }_{82}^{212} \mathrm{~Pb}\) d) \({ }_{84}^{216} \mathrm{Po} \longrightarrow{ }_{82}^{212} \mathrm{~Pb}+{ }_{1}^{0} \mathrm{e}\) \(e_{84}^{216} \mathrm{Po}+2_{-1}^{0} \mathrm{e} \longrightarrow{ }_{82}^{212} \mathrm{~Pb}+4_{0}^{1} \mathrm{n}\)

Short Answer

Expert verified
The correct nuclear equation is option (b): _{84}^{216} ext{Po} ightarrow _{82}^{212} ext{Pb} + _{2}^{4} ext{He}.

Step by step solution

01

Review the concept of alpha decay

Alpha decay is a type of radioactive decay where an alpha particle, which consists of 2 protons and 2 neutrons (equivalent to a helium nucleus, _{2}^{4} ext{He} ), is emitted from the nucleus. As a result, the mass number of the parent nucleus decreases by 4, and its atomic number decreases by 2.
02

Analyze the given options

In each option, examine the changes in atomic and mass numbers. In alpha decay: - The atomic number decreases by 2. - The mass number decreases by 4. Look for these specific changes in the options. The atomic number of Po is 84 and the mass number is 216, so after decay, the resulting atom should have an atomic number of 82 and a mass number of 212.
03

Identify the correct nuclear equation

Check each option: - Option (a): Atomic number decreases incorrectly (鈦1 e represents a beta particle, not an alpha particle). - Option (b): Correctly shows the emission of an alpha particle (鈦4 from mass number, 鈦2 from atomic number) - Option (c): Incorrect as it implies alpha particle is added, not emitted. - Option (d): Incorrect as it shows a beta particle emission. - Option (e): Incorrect as it involves electrons and neutrons which do not apply to this decay. Option (b) matches the correct changes for alpha decay.

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Key Concepts

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

Radioactive Decay
Radioactive decay is a natural and spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. It鈥檚 all about achieving stability. When a nucleus is unstable due to an imbalance in the number of protons and neutrons, it tends to undergo decay to reach a stable state. There are several types of radioactive decay:
  • Alpha Decay: Involves the emission of an alpha particle.
  • Beta Decay: Involves the emission of electrons or positrons.
  • Gamma Decay: Involves the emission of gamma rays.
Alpha decay is particularly pertinent when discussing the decay of heavy elements like polonium. Each decay process results in the formation of different elements or isotopes, as nuclear reactions transform the original nucleus. Understanding these mechanisms helps scientists predict the behavior of radioactive substances and utilize their properties in various fields like medicine and archaeology.
Nuclear Equations
Nuclear equations are similar to chemical equations, but instead, they show the changes within the nucleus during radioactive decay. These equations highlight the transformation of the original atomic nucleus, often with an emitted particle and a resultant nucleus.In a nuclear equation:
  • The mass number (top number) and the atomic number (bottom number) must be balanced on both sides of the equation.
  • Numbers must reflect the conservation of mass and charge.
For example, the nuclear equation representing alpha decay can be written as:\[ _{Z}^{A}X \rightarrow _{Z-2}^{A-4}Y + _{2}^{4}He \]Here, an alpha particle is emitted, which reduces the mass number by 4 and the atomic number by 2. The result is a different element with a lower atomic number. The equations are tools that help us visualize how an unstable element transforms during decay.
Polonium Decay
Polonium is a heavy, radioactive element that undergoes alpha decay to reach stability. One of its isotopes, Polonium-216, decays to form Lead-212. In the process of its decay:
  • Polonium-216 emits an alpha particle, \( _{2}^{4}He \), which consists of 2 protons and 2 neutrons.
  • This emission results in a reduction of both the atomic number and the mass number.
The nuclear equation for this decay is:\[ _{84}^{216}Po \rightarrow _{82}^{212}Pb + _{2}^{4}He \]Here, Polonium (\( _{84}^{216}Po \)) transforms into Lead (\( _{82}^{212}Pb \)) by emitting an alpha particle. The shift in numbers accounts for the emission of the alpha particle, aligning with the conservation laws in nuclear reactions.Understanding this transformation is crucial in fields that utilize radioactive decay, providing insight into the behavior of isotopes and their applications.

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Most popular questions from this chapter

The decay of \(\mathrm{Rb}-87\left(t_{1 / 2}=4.8 \times 10^{10} \mathrm{y}\right)\) to \(\mathrm{Sr}-87\) has been used to determine the age of ancient rocks and minerals. a) Write the balanced nuclear equation for this decay. If a sample of rock is found to be \(0.100 \%\) by mass \(\mathrm{Rb}-87\) and \(0.00250 \%\) by mass \(\mathrm{Sr}-87,\) what is the age of the rock? Assume that there was no \(\mathrm{Sr}-87\) present when the rock formed.

Rubidium- 87 , which forms about \(28 \%\) of natural rubidium, is radioactive, decaying by the emission of a single beta particle to strontium- 87 . Write the nuclear equation for this decay of rubidium- 87.

The gold-198 isotope is used in the treatment of brain, prostate, and ovarian cancer. Au-198 has a half-life of \(2.69 \mathrm{~d}\). If a hospital needs to have \(25 \mathrm{mg}\) of \(\mathrm{Au}-198\) on hand for treatments on a particular day, and shipping takes \(72 \mathrm{~h},\) what mass of \(\mathrm{Au}-198\) needs to be ordered?

Gamma radiation can be used to kill bacteria in food using a process called irradiation. There is concern on the part of some people that the irradiated food is radioactive. Why is this not the case? If you wanted to make the food radioactive, what would you have to do?

Radioisotope thermoelectric generators can be used by satellites to obtain power from radioactive decay of various isotopes, plutonium- 238 being the preferred fuel. Plutonium- 238 decays via alpha emission and has a halflife of 87.7 years. a) Write the nuclear equation for the alpha decay of plutonium-238. If you were to start with \(250.0 \mathrm{~g}\) of \(\mathrm{Pu}-238\) to power a satellite, what mass would remain after 45 years?

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