Question

In 2010, a team of scientists from Russia and the U.S. reported creation of the first atom of element 117 , which is not yet named and is denoted [117]. The synthesis involved the collision of a target of \({ }^{249}\) Bk with accelerated ions of an isotope which we will denote \(Q\). The product atom, which we will call \({ }_{97}^{249} \mathrm{Bk}+\mathrm{Q} \longrightarrow \mathrm{Z} \longrightarrow{ }_{117}^{294}[117]+3{ }_{0}^{1} \mathrm{n}\)

Short answer

The unknown isotope Q involved in the synthesis of element 117 through the given nuclear reaction is \(Q = {}_{20}^{42} \mathrm{Ca}\). This was determined using the principle of conservation of mass numbers and atomic numbers in nuclear reactions, which resulted in an atomic number of 20 and a mass number of 42 for isotope Q, corresponding to Calcium.

Step-by-step solution

Analyze the given reaction

Let's look at the given nuclear reaction and identify the atomic numbers and mass numbers in it: \({ }_{97}^{249} \mathrm{Bk}+\mathrm{Q} \longrightarrow { }_{117}^{294}[117]+3{ }_{0}^{1} \mathrm{n}\) The atomic number (Z) and mass number (A) of Bk are 97 and 249 respectively. The unknown isotope, Q, should have atomic and mass numbers such that they satisfy the conservation laws of nuclear reactions.

Conservation of Atomic Numbers

According to the conservation of atomic numbers, the sum of atomic numbers of reactants should be equal to the sum of atomic numbers of products. The equation we can write for the atomic number is: Z of Bk + Z of Q = Z of [117] + Z of n Here, the atomic number of n (neutron) is 0. Substituting the given values into the equation: 97 + Z of Q = 117. Solving for Z of Q: Z of Q = 117 - 97 = 20. So, the atomic number of isotope Q is 20.

Conservation of Mass Numbers

According to the conservation of mass numbers, the sum of mass numbers of reactants should be equal to the sum of mass numbers of products. The equation we can write for the mass number is: A of Bk + A of Q = A of [117] + 3 * A of n Here, the mass number of n (neutron) is 1. Substituting the given values into the equation: 249 + A of Q = 294 + 3. Solving for A of Q: A of Q = 294 - 249 - 3 = 42. So, the mass number of isotope Q is 42.

Identifying the element Q

Now, we have the atomic number (Z) and mass number (A) for the isotope Q. These are 20 and 42, respectively. Looking up the periodic table, the element with atomic number 20 is Calcium (Ca). Thus, the isotope of Ca involved in the collision is: \(Q = {}_{20}^{42} \mathrm{Ca}\)

Key concepts

Atomic Number

The atomic number is a fundamental concept in understanding elements on the periodic table. It represents the number of protons found in the nucleus of an atom. Each element has a unique atomic number, which defines its identity and position on the periodic table.
For example, in our original exercise, the element Bk (Berkelium) has an atomic number of 97. This means there are 97 protons in its nucleus. Identifying the atomic number of an unknown isotope, such as Q, is crucial for determining its identity. In the nuclear reaction provided, the conservation of atomic numbers helps us solve for the atomic number of Q, leading us to identify it as 20.

Mass Number

Mass number, unlike the atomic number, is not always unique for each element and can vary due to isotopes. The mass number is the total sum of protons and neutrons in an atom's nucleus.
Using our example, the mass number for Berkelium (Bk) is 249, denoted as "}_{97}^{249} . This exercise illustrates that the sum of the mass numbers in reactants must match that in the products. By applying this principle, we identified that isotope Q must have a mass number of 42 to satisfy the equation, confirming its identity as "}_{20}^{42} Calcium (Ca).
Mass numbers help distinguish between different isotopes of the same element, which can have differing numbers of neutrons but the same number of protons.

Isotope Identification

Isotopes are variants of elements that have the same number of protons but different numbers of neutrons. This results in differing mass numbers for the isotopes of a single element.
For instance, the exercise shows that isotope Q, identified as "}_{20}^{42} Calcium, is an isotope of Ca that differs from the more common "}_{20}^{40} Calcium due to having two additional neutrons.
Recognizing isotopes is crucial in nuclear chemistry because it affects the stability and behavior of the nucleus, especially in reactions like those used to synthesize new elements, as demonstrated with the creation of element 117.

Conservation Laws in Chemistry

The conservation laws, such as those of atomic and mass numbers, are foundational principles in chemical reactions and nuclear processes. For chemical reactions, the conservation of mass is critical. In nuclear reactions, similar conservation laws for atomic and mass numbers must be strictly observed.
In our exercise, these laws ensure that the number of each type of particle remains constant before and after the reaction. This involves balancing the atomic numbers to maintain elemental balance and aligning the mass numbers to account for all neutrons, protons, and formed products. Using these laws, we identified both the atomic (20) and mass numbers (42) of isotope Q, facilitating its identification as Calcium (Ca).
Understanding conservation laws allows chemists to predict the results of reactions and ensures that all changes are accurately accounted for in equations.