Question

Write the symbols for the following isotopes: (a) Its atoms contain 50 electrons and 70 neutrons. (b) Its atoms have \(A=56\) and \(Z=26\). (c) Its atoms have \(A=226\) and contain 88 electrons.

Short answer

(a) \(^{120}_{50}\text{Sn}\); (b) \(^{56}_{26}\text{Fe}\); (c) \(^{226}_{88}\text{Ra}\).

Step-by-step solution

Determine the Atomic Number for (a)

Given that an atom contains 50 electrons, its atomic number \(Z\) is 50 since the number of electrons equals the number of protons in a neutral atom. The element with atomic number 50 is tin (Sn).

Determine the Mass Number for (a)

The mass number \(A\) is the sum of protons and neutrons: \(A = Z + N\). Here, \(Z = 50\) and \(N = 70\). Therefore, the mass number is \(A = 50 + 70 = 120\).

Write the Symbol for Isotope (a)

The symbol for this isotope is \(^{120}_{50}\text{Sn}\).

Identify the Element and Isotope for (b)

Given \(A = 56\) and \(Z = 26\), the element with atomic number 26 is iron (Fe). This isotope is \(^{56}_{26}\text{Fe}\).

Determine the Atomic Number for (c)

The atom has 88 electrons, so its atomic number \(Z\) is 88 (since the number of electrons equals protons in a neutral atom). The element with atomic number 88 is radium (Ra).

Write the Symbol for Isotope (c)

Given \(A = 226\) and \(Z = 88\), the isotope is \(^{226}_{88}\text{Ra}\).

Key concepts

Atomic Number

The atomic number, represented as \( Z \), is a fundamental property of an element that tells us the number of protons in the nucleus of an atom. It is essentially the identity of an element, as each element on the periodic table has a unique atomic number. For example, if an atom has an atomic number of 50, it means there are 50 protons in its nucleus. This also implies there are 50 electrons orbiting the nucleus when the atom is neutral, as the number of electrons equals the number of protons. Knowing the atomic number helps us identify the element directly from the periodic table.

• The element with \( Z = 50 \) is tin (Sn).
• The element with \( Z = 26 \) is iron (Fe).
• The element with \( Z = 88 \) is radium (Ra).

Understanding atomic numbers is crucial as it lays the foundation for exploring other nuclear properties, such as isotopes and mass number.

Mass Number

The mass number, denoted by \( A \), indicates the total number of protons and neutrons in an atom's nucleus. Unlike the atomic number, which is fixed for a particular element, the mass number can vary because the number of neutrons can differ among atoms of the same element, resulting in isotopes. The formula for calculating mass number is:\[A = Z + N\]where \( N \) is the number of neutrons.For instance:

• If an atom of tin (Sn) has \( Z = 50 \) and \( N = 70 \), then \( A = 50 + 70 = 120 \).
• For iron (Fe) with \( Z = 26 \) and \( A = 56 \), the number of neutrons is \( N = 56 - 26 = 30 \).
• Radium (Ra), with \( Z = 88 \) and \( A = 226 \), has \( N = 226 - 88 = 138 \) neutrons.

The mass number helps in writing the isotope notation, which gives a complete picture of an atom's composition.

Neutral Atom

A neutral atom is defined as an atom where the number of protons (positively charged particles) equals the number of electrons (negatively charged particles). As a result, the overall electric charge of the atom is zero. This balance between protons and electrons ensures that the atom does not carry an excess positive or negative charge, maintaining its neutrality. For example:

• An atom with \( Z = 50 \) has 50 protons and 50 electrons, making it neutral.
• The same principle applies to an iron atom with \( Z = 26 \); it has 26 protons and 26 electrons.
• Likewise, a radium atom with \( Z = 88 \) has 88 protons balanced by 88 electrons.

Ensuring neutrality is crucial for chemical stability and plays a significant role in the chemical behavior of atoms. Understanding the concept of a neutral atom is key when studying atomic structure and reactions.