Question

In 1974 , a team of Russian physicists smashed a chromium-54 nucleus into a lead-207 target. If a new element, \(X,\) and one neutron were produced from the collision, what nuclide did the team create?

Short answer

The nuclide created is Seaborgium-260 (\( \text{Sg}^{260}_{106} \)).

Step-by-step solution

Understanding the Initial Equation

First, we need to understand that a chromium-54 nucleus (\( \text{Cr}^{54}_{24} \)) is colliding with a lead-207 nucleus (\( \text{Pb}^{207}_{82} \)). The resulting equation should include a new element \( X \) and a neutron, \( n^1_0 \). The neutron carries no charge and has a mass number of 1.

Balancing the Mass Numbers

In a collision that produces a single neutron, the sum of mass numbers before the collision must equal the sum of mass numbers after the collision. The mass numbers on the left are 54 (from Cr) and 207 (from Pb), adding up to 261. For the products, we have the new element \(X\) with an unknown mass number \(A\), and one neutron with mass number 1, so:\[ A + 1 = 261 \]Solving this, \(A = 260 \).

Balancing the Atomic Numbers

Similarly, the atomic numbers must also balance. Before the reaction, the atomic numbers are 24 (from Cr) and 82 (from Pb), totaling 106. For the products, the atomic number of the new element \( X \) is \( Z \), and the neutron is neutral, so:\[ Z + 0 = 106 \]Hence, \( Z = 106 \).

Identifying the Element

The element with atomic number 106 is Seaborgium (symbol \( Sg \)). Thus, the nuclide produced is \( \text{Sg}^{260}_{106} \).

Key concepts

Atomic Structure

Atoms are the basic building blocks of matter, composed of three primary particles: protons, neutrons, and electrons. Understanding these particles is crucial when dealing with nuclear reactions, such as the example given with the collision of a chromium-54 nucleus with a lead-207 nucleus.

• Protons carry a positive charge and define the atomic number, which determines the element. In nuclear reactions, the atomic numbers need to balance during the reaction to maintain the electrical neutrality.
• Neutrons are neutral, having no charge, but they contribute to the atomic mass. The sum of protons and neutrons equals the mass number of an atom.
• Electrons are negatively charged and orbit the nucleus but do not play a direct role in nuclear reaction equations. Their number equals the protons in a neutral atom.

A balanced nuclear reaction must conserve both the total atomic number and total mass number, as demonstrated in the example problem, where a collision yields a new element while satisfying these conservation laws.

Nuclear Physics

Nuclear physics focuses on understanding the constituents and interactions of atomic nuclei. It involves studying how these interactions lead to various nuclear phenomena, such as the transformation of elements during collisions. In the exercise, a fascinating nuclear reaction occurs as a chromium nuclide collides with a lead nuclide, producing a new element. This process is governed by conservation laws:

• Conservation of Mass Number: The sum of mass numbers of reactants and products must be equal. This principle helped identify the mass number of the unknown element as 260.


• Conservation of Atomic Number: By ensuring that the sum of atomic numbers remains consistent, the new element's atomic number was pinpointed at 106.

Nuclear reactions such as this allow scientists to explore stable and unstable nuclides, enhancing our understanding of atomic interactions and leading to discoveries of new elements and isotopes.

Element Identification

Element identification involves determining the type of element based on its atomic number and understanding its properties. In nuclear reactions like the one explored here, identifying new elements is a critical step. By solving the exercise, we identified an element with an atomic number of 106 and a mass number of 260. This corresponds to the chemical element Seaborgium (Sg).

• Atomic Number: The atomic number is the count of protons in an atom's nucleus. It defines the element's identity and position in the periodic table.


• Mass Number: Adding protons and neutrons gives the mass number. It helps distinguish between isotopes of the same element.

Identifying elements based on nuclear reactions is essential in expanding our periodic table and understanding the nature of newly synthesized elements, providing insight into their stability and potential applications.