Problem 105 - Introductory Chemistry Atoms First

Question

Complete these equations representing nuclear reactions: (a) \({ }_{51}^{121} \mathrm{Sb}+{ }_{2}^{4} \mathrm{He} \rightarrow ?+{ }_{1}^{1} \mathrm{H}\) (b) \({ }_{13}^{27} \mathrm{Al}+{ }_{2}^{4} \mathrm{He} \rightarrow ?+{ }_{0}^{1} \mathrm{n}\) (c) \({ }_{92}^{238} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \rightarrow ?+{ }_{-1}^{0} \mathrm{e}\)

Step-by-Step Solution

Answer

(a) \({ }_{51}^{121} \mathrm{Sb}+{ }_{2}^{4} \mathrm{He} \rightarrow { }_{52}^{124} \mathrm{Te} +{ }_{1}^{1} \mathrm{H}\) (b) \({ }_{13}^{27} \mathrm{Al}+{ }_{2}^{4} \mathrm{He} \rightarrow { }_{15}^{30} \mathrm{P} +{ }_{0}^{1} \mathrm{n}\) (c) \({ }_{92}^{238} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \rightarrow { }_{93}^{239} \mathrm{Np} +{ }_{-1}^{0} \mathrm{e}\)

Step 1: Balance mass numbers

Sum the mass numbers of the reactants and subtract the mass number of the known product: \(121 + 4 - 1 = 124\)

Step 2: Balance atomic numbers

Sum the atomic numbers of the reactants and subtract the atomic number of the known product: \(51 + 2 - 1 = 52\)

Step 3: Identify the element with the atomic number

The element with the atomic number 52 is Tellurium (Te). So the complete reaction is: \({ }_{51}^{121} \mathrm{Sb}+{ }_{2}^{4} \mathrm{He} \rightarrow { }_{52}^{124} \mathrm{Te} +{ }_{1}^{1} \mathrm{H}\) (b) \({ }_{13}^{27} \mathrm{Al}+{ }_{2}^{4} \mathrm{He} \rightarrow ?+{ }_{0}^{1} \mathrm{n}\)

Step 1: Balance mass numbers

Sum the mass numbers of the reactants and subtract the mass number of the known product: \(27 + 4 - 1 = 30\)

Step 2: Balance atomic numbers

Sum the atomic numbers of the reactants and subtract the atomic number of the known product: \(13 + 2 - 0 = 15\)

Step 3: Identify the element with the atomic number

The element with the atomic number 15 is Phosphorus (P). So the complete reaction is: \({ }_{13}^{27} \mathrm{Al}+{ }_{2}^{4} \mathrm{He} \rightarrow { }_{15}^{30} \mathrm{P} +{ }_{0}^{1} \mathrm{n}\) (c) \({ }_{92}^{238} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \rightarrow ?+{ }_{-1}^{0} \mathrm{e}\)

Step 1: Balance mass numbers

Sum the mass numbers of the reactants and subtract the mass number of the known product: \(238 + 1 - 0 = 239\)

Step 2: Balance atomic numbers

Sum the atomic numbers of the reactants and subtract the atomic number of the known product: \(92 + 0 - (-1) = 93\)

Step 3: Identify the element with the atomic number

The element with the atomic number 93 is Neptunium (Np). So the complete reaction is: \({ }_{92}^{238} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \rightarrow { }_{93}^{239} \mathrm{Np} +{ }_{-1}^{0} \mathrm{e}\)

Key Concepts

Mass Number

In nuclear reactions, the mass number is essential for balancing nuclear equations. The mass number represents the total number of protons and neutrons in an atomic nucleus. In an element's nuclear symbol, it is the number found at the upper left corner. To achieve a balanced nuclear reaction, the sum of the mass numbers of the reactants must equal the sum of the mass numbers of the products.
For example, consider the reaction involving antimony, helium, and the formation of tellurium and hydrogen:

• The mass numbers of the reactants, 121 (Sb) and 4 (He), are added.
• The mass number of the known product, 1 (H), is subtracted.
• This results in a total mass number of 124 for the unknown product, indicating Element Te has a mass number of 124.

Understanding the mass number helps in visualizing how atomic particles are conserved in a nuclear reaction, even though their identities may change.

Atomic Number

The atomic number is the count of protons in an atom's nucleus and uniquely identifies a chemical element. In the context of nuclear reactions, it is crucial for determining which elements are involved and what transformations occur.
In the nuclear reaction involving aluminum and helium, where phosphorus and neutrons are produced, the atomic numbers play a pivotal role:

• Add the atomic numbers of aluminum (13) and helium (2).
• Subtract the atomic number of the neutron (0).
• The resulting atomic number is 15, pinpointing that the element with the atomic number of 15 is phosphorus, represented as P.

This value ensures that the charge before and after the reaction is balanced, reflecting the scientific principle that the total number of protons must be conserved in a nuclear reaction.

Neutron

Neutrons are subatomic particles found in the nucleus of an atom, with no electrical charge and a similar mass to protons. They are a key component of nuclear reactions, influencing stability and the types of reactions that occur.
In context, consider a reaction involving uranium and a neutron leading to neptunium and an electron:

• Adding a neutron ( _{0}^{1}n) to uranium ( _{92}^{238}U) increases the total mass number from 238 to 239.
• The neutron does not change the atomic number because it carries no charge.
• When the reaction produces an electron, the atomic number of the product neptunium becomes 93 — neutron presence indirectly influencing this increment.

Neutrons act as facilitators of nuclear reactions, leading to the creation of different elements while ensuring mass number alignment across the reaction.