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Chapter 45: Problem 30

An important reaction results when lithium absorbs a proton and splits into two helium nuclei (alpha particles). Write out the appropriate equation describing the event.

Short Answer

Expert verified
The nuclear reaction is: \(^7_3\text{Li} + ^1_1\text{p} \rightarrow 2\,^4_2\text{He}\).

Step by step solution

01

Identify the Reactants

In the given reaction, lithium absorbs a proton. Lithium is represented symbolically as \(^7_3\text{Li}\), meaning it has 3 protons and 4 neutrons. The proton absorbed is represented as \(^1_1\text{p}\).
02

Identify the Products

The reaction results in the formation of two helium nuclei, which are alpha particles. Each helium nucleus is represented as \(^4_2\text{He}\). Since two helium nuclei are produced, in the reaction, we represent them as \(2\,^4_2\text{He}\).
03

Write the Nuclear Reaction Equation

In a nuclear reaction, the sum of mass numbers (top numbers) and atomic numbers (bottom numbers) must be balanced on both sides of the equation. The reaction can be written as \(^7_3\text{Li} + ^1_1\text{p} \rightarrow 2\,^4_2\text{He}\). We can verify the balance: on the left side, the total mass number is \(7 + 1 = 8\) and the atomic number is \(3 + 1 = 4\). On the right side, for the helium nuclei, \(2 \times 4 = 8\) and \(2 \times 2 = 4\), ensuring both mass and atomic numbers are conserved.

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Key Concepts

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

Lithium Reactions
Lithium is a fascinating element that often participates in nuclear reactions. One interesting reaction occurs when lithium absorbs a proton. In this case, the lithium nucleus undergoes a transformation and splits into two helium nuclei. This process is intriguing because it highlights how elements can change in nuclear reactions. Lithium in this context is represented by its isotope notation
  • It has 3 protons, indicated by the bottom number in the symbol
  • It has 4 neutrons, which can be calculated from subtracting the number of protons from the top number, the mass number
The absorption of a proton can cause lithium to transform significantly, showcasing the dynamic nature of nuclei in nuclear physics.
Alpha Particles
Alpha particles are a crucial part of many nuclear reactions. They are essentially helium nuclei, made up of 2 protons and 2 neutrons. This is why they are often denoted by the symbol
  • Each alpha particle has a mass number of 4, because it adds up the protons and neutrons
  • The atomic number is 2, representing the number of protons
These particles are a significant product of nuclear reactions, including the one involving lithium described here. They are released in nuclear decay processes and have more mass than beta or gamma radiation, affecting their penetration power, which is relatively low among the types of nuclear radiation.
Helium Nuclei
Helium nuclei, also known as alpha particles, play a significant role in nuclear reactions, such as the division of lithium after proton absorption. Each helium nucleus is stable and small, leading it to be released easily during nuclear events. In many nuclear reactions, helium nuclei form as stable daughters from parent nuclei changes. Their stability makes them excellent examples of simple nuclear structures. The helium nucleus's stability stems from its balanced configuration of equal protons and neutrons, creating a tightly bound, low-energy state. The formation of helium nuclei in reactions emphasizes nuclear processes in everyday stellar and nuclear physics.
Nuclear Equations
Nuclear equations are essential for describing the changes in nuclear reactions accurately. In these equations, the conservation of mass and atomic numbers must be adhered to. This means, when writing a nuclear equation:
  • The sum of the mass numbers on the reactant side must equal that on the product side
  • The same goes for atomic numbers, ensuring a balanced equation
In the lithium and proton reaction, for example, the equation ensures that
  • Both mass (top number) and atomic numbers (bottom number) are correctly accounted for, showing conservation
Understanding and writing nuclear equations help in grasping the principles of nuclear chemistry and physics, rooting the process in predictable, calculable results.

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Most popular questions from this chapter

Using the exponential function. The curve is an exponential decay curve, and it is expressed by the equation $$ \frac{N}{N_{0}}=e^{-\lambda t} $$ where \(\lambda\) is the decay constant, and \(N / N_{0}\) is the fraction of the original \(N_{0}\) particles that remain undecayed after a time \(t\). Inasmuch as \(\lambda t_{1 / 2}=0.693, \lambda=0.693 / t_{1 / 2}=0.132 /\) year and \(N / N_{0}=\) 0.333. Thus, $$ 0.333=e^{-0.132 t / y e a r} $$ Take the natural logarithm of each side to find $$ \ln (0.333)=-0.132 t / \text { year } $$ from which \(t=8.3\) years.

Determine the parent nuclide (P) that decayed into thorium-234 as follows: $$ \mathrm{P} \rightarrow^{234} \mathrm{Th}+\alpha $$

By natural radioactivity \({ }^{238} \mathrm{U}\) emits an \(\alpha\) -particle. The heavy residual nucleus is called \(\mathrm{UX}_{1} . \mathrm{UX}_{1}\) in turn emits a beta particle. The resultant nucleus is called \(\mathrm{UX}_{2} .\) Determine the atomic number and mass number for \((a) \mathrm{UX}_{1}\) and \((b) \mathrm{UX}_{2}\).

How many protons, neutrons, and electrons are there in \((a){ }^{3} \mathrm{He}\), (b) \(^{12} \mathrm{C}\), and \((c)^{206} \mathrm{~Pb}\) ? (a) The atomic number of He is 2; therefore, the nucleus must contain 2 protons. Since the mass number of this isotope is 3 , the sum of the protons and neutrons in the nucleus must equal 3; therefore, there is 1 neutron. The number of electrons in the atom is the same as the atomic number, 2 . (b) The atomic number of carbon is 6 ; hence, the nucleus must contain 6 protons. The number of neutrons in the nucleus is equal to \(12-6=6\). The number of electrons is the same as the atomic number, 6 . (c) The atomic number of lead is 82 ; hence, there are 82 protons in the nucleus and 82 electrons in the atom. The number of neutrons is \(206-82=124\).

Astatine-215 has a half-life of \(100 \mu \mathrm{s}\). Determine the decay constant \((\lambda)\).
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