Question

Which of the following nuclear equations is(are) correct? a. \({ }_{4}^{7} \mathrm{Be} \rightarrow{ }_{3}^{7} \mathrm{Li}+{ }_{-1}^{0} \mathrm{e}\) b. \({ }_{5}^{8} \mathrm{~B} \rightarrow{ }_{4}^{8} \mathrm{Be}+{ }_{1}^{0} \mathrm{e}\) c. \({ }_{94}^{239} \mathrm{Pu}+{ }_{2}^{4} \mathrm{He} \rightarrow{ }_{96}^{242} \mathrm{Cm}+{ }_{1}^{1} \mathrm{H}\) d. \({ }_{43}^{97} \mathrm{Tc}+{ }_{-1}^{0} \mathrm{e} \rightarrow{ }_{42}^{97} \mathrm{Mo}\) e. \({ }_{4}^{7} \mathrm{Be}+{ }_{-1}^{0} \mathrm{e} \rightarrow{ }_{3}^{7} \mathrm{Li}\)

Short answer

The correct nuclear equations are (b) \({}_{5}^{8}\mathrm{~B}\rightarrow{}_{4}^{8}\mathrm{Be}+{}_{1}^{0}\mathrm{e}\), (d) \({}_{43}^{97}\mathrm{Tc}+{}_{-1}^{0}\mathrm{e}\rightarrow{}_{42}^{97}\mathrm{Mo}\), and (e) \({}_{4}^{7}\mathrm{Be}+{}_{-1}^{0}\mathrm{e}\rightarrow{}_{3}^{7}\mathrm{Li}\).

Step-by-step solution

Check Equation (a)

For nuclear reaction to be correct, the atomic numbers and mass numbers on both sides of the equation need to be equal. Let's check this for the first equation: \({}_{4}^{7}\mathrm{Be}\rightarrow{}_{3}^{7}\mathrm{Li}+{}_{-1}^{0}\mathrm{e}\). On the left side of the equation, the atomic number is 4 and the mass number is 7. On the right side, the sum of the atomic numbers is \(3+(-1)=2\) and the sum of the mass numbers is \(7+0=7\). The atomic numbers on both sides of the equation aren't equal, therefore the equation is incorrect.

Check Equation (b)

Let's check the second equation: \({}_{5}^{8}\mathrm{~B}\rightarrow{}_{4}^{8}\mathrm{Be}+{}_{1}^{0}\mathrm{e}\). On the left side of the equation, the atomic number is 5 and the mass number is 8. On the right side, the sum of the atomic numbers is \(4+1=5\) and the sum of the mass numbers is \(8+0=8\). This equation is correct as the atomic numbers and mass numbers on both sides of the equation are equal.

Check Equation (c)

Next, let's check the third equation: \({}_{94}^{239}\mathrm{Pu}+{}_{2}^{4}\mathrm{He}\rightarrow{}_{96}^{242}\mathrm{Cm}+{}_{1}^{1}\mathrm{H}\). On the left side of the equation, the sum of atomic numbers is \(94+2=96\) and sum of mass numbers is \(239+4=243\). On the right side, the sum of atomic numbers is \(96+1=97\) and sum of mass numbers is \(242+1 =243\). The atomic numbers on both sides of the equation aren't equal, therefore the equation is incorrect.

Check Equation (d)

Now let's check the fourth equation: \({}_{43}^{97}\mathrm{Tc}+{}_{-1}^{0}\mathrm{e}\rightarrow{}_{42}^{97}\mathrm{Mo}\). On the left side of the equation, the sum of atomic numbers is \(43+(-1) =42 \) and the mass number is 97. On the right side, the atomic number is 42 and the mass number is 97. This equation is correct as the atomic numbers and mass numbers on both sides of the equation are equal.

Check Equation (e)

Finally, let's check the fifth equation: \({}_{4}^{7}\mathrm{Be}+{}_{-1}^{0}\mathrm{e}\rightarrow{}_{3}^{7}\mathrm{Li}\). On the left side of the equation, the sum of atomic numbers is \(4+(-1) = 3 \) and the sum of mass numbers is \(7+0=7 \). On the right side, the atomic number is 3 and the mass number is 7. This equation is correct as the atomic numbers and mass numbers on both sides of the equation are equal. So, the correct nuclear equations are equation (b), (d), and (e).

Key concepts

Atomic Numbers

In nuclear equations, atomic numbers represent the number of protons present in the nucleus of an atom. It is shown as the subscript on the left side of an element's symbol. Atomic numbers are crucial because they determine the identity of an element. For instance, in the given equation \[{}_{4}^{7}\mathrm{Be}\rightarrow{}_{3}^{7}\mathrm{Li}+{}_{-1}^{0}\mathrm{e}\]"Beryllium" has an atomic number of 4, indicating it has 4 protons. When checking nuclear reactions, we must ensure that the sum of atomic numbers, representing protons across all reactants, equals the sum on the product side. This conservation ensures that the identities of the elements are maintained throughout the reaction.

Mass Numbers

Mass numbers indicate the total number of protons and neutrons in the nucleus of an atom, shown as the superscript to the left of an element's symbol. They are essential in balancing nuclear equations as they represent the mass of an atom.In the equation example:\[{}_{5}^{8}\mathrm{~B}\rightarrow{}_{4}^{8}\mathrm{Be}+{}_{1}^{0}\mathrm{e} \]The element 'Boron' has a mass number of 8, highlighting its sum of protons and neutrons. During nuclear reactions, the total mass number from the reactants should equal the total mass from the products. This conservation ensures that mass is balanced in the equation, which is a key aspect in analyzing nuclear reactions effectively.

Balancing Equations

Balancing an equation, especially nuclear equations, involves making sure that both sides of the equation have equal total atomic and mass numbers. For equations to be correct in nuclear chemistry, balance must involve two aspects:

• Conservation of Atomic Numbers: The sum of atomic numbers (protons) on one side must equal the sum on the other.
• Conservation of Mass Numbers: The total mass numbers (protons + neutrons) on one side must equal that on the other.

For example, analyzing equation (d):\[{}_{43}^{97}\mathrm{Tc}+{}_{-1}^{0}\mathrm{e}\rightarrow{}_{42}^{97}\mathrm{Mo}\]Both atomic and mass numbers are conserved, making it a correctly balanced nuclear equation. Balancing helps understand how elements transform in reactions and predict the outcome of nuclear processes.

Nuclear Reactions

Nuclear reactions refer to processes where the nuclei of atoms change due to collision or decay. These reactions can result in the transformation of elements into different elements, releasing or absorbing a significant amount of energy. Key types of nuclear reactions include:

• Nuclear Decay: Spontaneous transformation where an unstable nucleus emits particles, such as alpha, beta, or gamma particles.
• Nuclear Fission: Splitting of larger atomic nuclei into smaller parts, releasing energy, often used in energy generation.
• Nuclear Fusion: Combining small atomic nuclei to form a larger one, releasing energy, mostly occurring in stars.

In our equations, transformations showcase how an atom can emit or absorb particles resulting in different elements or isotopes. Understanding these reactions is central to fields like nuclear energy and radioactive decay analysis.