Question

Write the correct symbol, with both superscript and subscript, for each of the following. Use the list of elements in the front inside cover as needed: (a) the isotope of platinum that contains 118 neutrons, (b) the isotope of krypton with mass number 84, (c) the isotope of arsenic with mass number 75 , (d) the isotope of magnesium that has an equal number of protons and neutrons.

Short answer

The correct symbols with both superscript and subscript for each isotope are: (a) \(_{78}^{196}\textrm{Pt}\) - the isotope of platinum that contains 118 neutrons (b) \(_{36}^{84}\textrm{Kr}\) - the isotope of krypton with mass number 84 (c) \(_{33}^{75}\textrm{As}\) - the isotope of arsenic with mass number 75 (d) \(_{12}^{24}\textrm{Mg}\) - The isotope of magnesium that has an equal number of protons and neutrons

Step-by-step solution

Find the atomic number of the elements

Using the list of elements, find the atomic number (number of protons) of platinum, krypton, arsenic, and magnesium.

Find the mass number for each isotope

For each isotope, use the given information to find the mass number, which is the sum of the number of protons and neutrons. (a) The isotope of platinum that contains 118 neutrons:

Step 2a: Find the mass number for the platinum isotope

Using the atomic number of platinum (symbol: Pt, atomic number: 78) and the given number of neutrons (118), calculate the mass number for this isotope of platinum: Mass number = Atomic number (number of protons) + number of neutrons = 78 + 118 = 196 (b) The isotope of krypton with mass number 84:

Step 2b: Use the given mass number for the krypton isotope

Given the mass number of this krypton isotope (symbol: Kr, atomic number: 36) is 84, we don't need to calculate anything else. (c) The isotope of arsenic with mass number 75:

Step 2c: Use the given mass number for the arsenic isotope

Given the mass number of this arsenic isotope (symbol: As, atomic number: 33) is 75, we don't need to calculate anything else. (d) The isotope of magnesium that has an equal number of protons and neutrons:

Step 2d: Find the mass number for the magnesium isotope

Since this magnesium isotope has an equal number of protons and neutrons, the mass number is twice the atomic number. From Step 1, we know that magnesium (symbol: Mg) has an atomic number of 12. Therefore, the mass number of this isotope is: Mass number = 2 * Atomic number = 2 * 12 = 24

Write the correct symbol with both superscript and subscript for each isotope

Now we have the mass numbers and atomic numbers of each isotope. We can write them in the form A_ZX, where A is the mass number, Z is the atomic number, and X is the element symbol. The symbol looks like this: \(_{Z}^{A}X\) (a) \(_{78}^{196}\textrm{Pt}\) - the isotope of platinum that contains 118 neutrons (b) \(_{36}^{84}\textrm{Kr}\) - the isotope of krypton with mass number 84 (c) \(_{33}^{75}\textrm{As}\) - the isotope of arsenic with mass number 75 (d) \(_{12}^{24}\textrm{Mg}\) - The isotope of magnesium that has an equal number of protons and neutrons

Key concepts

Mass number

The mass number is a fundamental concept in understanding isotopes. It represents the total number of protons and neutrons present in the nucleus of an atom.
The mass number is always a whole number and is noted as the superscript to the left of the chemical symbol in isotopic notation.

For example, in the isotope notation for platinum \(_{78}^{196}\text{Pt}\), the mass number is 196. This tells us there are 196 protons and neutrons combined in the platinum nucleus.

The mass number is crucial for distinguishing between different isotopes of an element. This is because isotopes of an element have the same number of protons (same atomic number) but differ in the number of neutrons. Therefore, they have different mass numbers.

• Mass number = number of protons + number of neutrons
• It helps in identifying and differentiating isotopes

Understanding mass numbers helps us follow chemical reactions and nuclear processes closely, as these involve changes inside atomic nuclei rather than in their outer orbits.

Atomic number

The atomic number is a defining attribute of an element. It tells us the number of protons in the nucleus of an atom.
This number is unique to each element and determines the chemical properties of the element. It is shown as the subscript to the left of the chemical symbol when writing isotopic notation.

For example, in the notation of krypton \(_{36}^{84}\text{Kr}\), the atomic number is 36. This indicates that every atom of krypton has 36 protons in its nucleus.

Since the atomic number defines the element, changing it would result in a completely different element. Here are some quick facts about atomic numbers:

• Atomic number = number of protons
• Defines the identity of an element
• Determines the position of the element in the periodic table

The consistency of the atomic number across isotopes of an element highlights fundamental stability in the universe’s elemental makeup.

Neutrons

Neutrons are subatomic particles found in the nucleus of an atom. They carry no electric charge, which is why their presence in the nucleus doesn’t change the element's atomic number.

However, varying numbers of neutrons lead to the formation of different isotopes of an element. For instance, platinum can have isotopes with more or fewer neutrons than its most common form. In the isotope notation\(_{78}^{196}\text{Pt}\), the mass number is 196, while the atomic number is 78. So:

• The number of neutrons = mass number - atomic number = 196 - 78 = 118

Neutrons play an important role in nuclear stability.
Too many or too few neutrons compared to protons can lead to radioactive decay.
Understanding neutrons helps explain why some isotopes are unstable and what happens during nuclear reactions. Neutrons are key players in nuclear fusion and fission processes, which are significant in both scientific research and nuclear energy production.