Question

Identify the isotope \(X\) that has one more neutron than protons and a mass number equal to nine times the charge on the ion \(X^{3+}\)

Short answer

There seems to be an error in the problem as the conditions do not provide a valid result.

Step-by-step solution

Define the conditions

Firstly, let's establish the conditions outlined in the question. \(X\) is an isotope, meaning it has a certain number of protons and a different number of neutrons. We know that \(X\) has one more neutron than proton, so we can state that the number of neutrons = number of protons + 1. Furthermore, the mass number of an isotope \(X\) is the sum of protons and neutrons, and it's given as nine times the charge on \(X^{3+}\). The ion \(X^{3+}\) indicates that there are 3 fewer electrons than protons, hence its atomic number (proton number) is 3.

Determine the proton and neutron number

From the above analysis, the number of protons is equal to 3 (atomic number). Since the number of neutrons is one more than the number of protons (from the problem statement), the number of neutrons is equal to 3 + 1 = 4.

Compute the mass number

Next, we calculate the mass number of \(X\) which is the sum of protons (3) and neutrons (4). This comes out to be 7.

Check the mass number condition

Finally, we need to verify if the mass number (7) is equal to nine times the charge on \(X^{3+}\). Since the charge on \(X^{3+}\) is of +3, nine times this charge is 27. This does not equal to our calculated mass number (7) which indicates a mistake in our calculation.

Key concepts

mass number

The mass number of an isotope is a vital concept in chemistry and physics. It represents the total count of protons and neutrons in an atom's nucleus. These subatomic particles are the heaviest parts of an atom, contributing significantly to its mass. Thus, the mass number is not to be confused with atomic mass, which considers the average mass of all isotopes of an element.
Understanding the mass number helps us determine the identity and isotope of an element. In isotopes, atoms of the same element have the same number of protons but differ in neutrons. This difference results in varying mass numbers even though the chemical behavior remains consistent.
For instance, an isotope of an element may have a mass number calculated by the equation: \( ext{mass number} = ext{number of protons} + ext{number of neutrons} \). The problem statement gives us a certain isotope condition where its mass number should equate to specific conditions involving its ionic charge. Continuous tracking of such quantities remains crucial when solving isotope-related exercises.

protons and neutrons

Protons and neutrons are fundamental components of an atom's nucleus, and they have significant roles in determining an element's properties. Protons are positively charged particles, while neutrons are neutral. The number of protons determines the element's identity, as well as its atomic number, which we will cover in more detail in the next section.
Neutrons stabilize the nucleus; they interact with protons—and other neutrons—via nuclear forces. Isotopes have differing numbers of neutrons but share the same proton count. This unique feature leads to variations in atoms' physical properties, while their chemical properties remain generally unchanged.
The interaction between protons and neutrons is described through the condition in the problem: The number of neutrons equals the number of protons plus one. This relationship is a common step in identifying isotopes and sets the stage for calculating the mass number.

atomic number

The atomic number is the cornerstone of an element's identity in the periodic table. Simplified, it is the count of protons in the nucleus of an atom. Since atoms are generally neutral, the atomic number also tells us the number of electrons surrounding the nucleus.
In isotopic terms, differing neutron counts among isotopes do not affect the atomic number. Thus, although isotopes like those discussed in the step-by-step solution have different neutron numbers, their atomic number remains the same because their proton count is invariant.

• Atomic number is unique for each element.
• Protons provide positive charge; thus, in ions where electrons are lost or gained, the atom will exhibit a charge.
• For example, a 3+ charge in the ion indicates a deficiency of 3 electrons relative to protons.

Understanding atomic numbers allows for accurate identification of elements and proper calculation in isotope-related equations where electron-proton balance is crucial.