Question

Elemental boron is composed of two isotopes, boron- 10 and boron-11. (a) How many protons and neutrons are found in these two isotopes of boron? (b) Write the correct isotopic notation for each of these isotopes of boron. (c) Calculate the mass percent of protons in the nucleus of each of these isotopes.

Short answer

Boron has 5 protons. Boron-10 has 5 neutrons, and boron-11 has 6 neutrons. The isotopic notations are \( ^{10}_{5}B \) and \( ^{11}_{5}B \). The mass percent of protons is 50% for boron-10 and approximately 45.45% for boron-11.

Step-by-step solution

- Identify the number of protons in boron

For both isotopes of boron, the number of protons is equal to the atomic number of boron, which is 5. This is consistent for all isotopes of an element.

- Calculate the number of neutrons for each isotope

The number of neutrons in an isotope is found by subtracting the atomic number from the mass number of the isotope. For boron-10, it is 10 (mass number) - 5 (atomic number) = 5 neutrons. For boron-11, it is 11 - 5 = 6 neutrons.

- Write the isotopic notation for boron-10

The isotopic notation includes the element's symbol, the mass number, and the atomic number. For boron-10, the isotopic notation is \( ^{10}_{5}B \).

- Write the isotopic notation for boron-11

Similarly, the isotopic notation for boron-11 is \( ^{11}_{5}B \).

- Calculate the mass percent of protons in boron-10

The mass percent of protons in an isotope is given by the formula \(\left( \frac{\text{number of protons}}{\text{mass number}} \right) \times 100\% \). For boron-10, it is \(\left( \frac{5}{10} \right) \times 100\% = 50\% \).

- Calculate the mass percent of protons in boron-11

Using the same formula for boron-11, it is \(\left( \frac{5}{11} \right) \times 100\% \approx 45.45\% \).

Key concepts

Isotopic Notation

Isotopic notation is a method used to represent the identity and atomic mass of isotopes. It includes the chemical symbol of the element, the mass number (total number of protons and neutrons) at the top, and the atomic number (total number of protons) at the bottom. For example, for boron-10, the isotopic notation is expressed as \( ^{10}_{5}B \), where 'B' stands for boron, '10' is the mass number, and '5' is the atomic number. This representation helps quickly convey the structure of the nucleus of an isotope.

Understanding isotopic notation is fundamental to chemistry and physics because it provides a precise way to identify different isotopes of an element, which can exhibit various properties and behaviors due to their differing neutron counts.

Atomic Number

The atomic number is a crucial concept in chemistry representing the number of protons found in the nucleus of an atom. It is designated by the letter 'Z'. For all isotopes of an element, the atomic number remains constant. In the case of boron, the atomic number is 5. This means that every isotope of boron, including boron-10 and boron-11, contains exactly 5 protons in its nucleus.

The atomic number uniquely identifies an element and determines its position in the periodic table. Not only does it tell us about the positive charge of the nucleus, but it also informs us about the number of electrons in a neutral atom, which defines the chemical behavior of the element.

Mass Number

The mass number, denoted as 'A', is the total count of protons and neutrons in an atom's nucleus. It differs for isotopes of the same element since they can have varying numbers of neutrons. The mass number is always a whole number and appears as the superscript in isotopic notation. For instance, in boron-10, the mass number is '10', indicating it has a combination of 10 protons and neutrons.

Knowing the mass number is essential to distinguish between isotopes and to calculate the number of neutrons by subtracting the atomic number from the mass number. This value is important for nuclear physics and chemistry as it affects the atomic mass and stability of an isotope.

Neutron Calculation

To calculate the number of neutrons in an isotope, one must subtract the atomic number from the mass number. For boron isotopes, the calculations are straightforward: boron-10 has 5 neutrons (10 - 5 = 5), and boron-11 has 6 neutrons (11 - 5 = 6).

Understanding how to calculate the number of neutrons is crucial, as neutrons play a significant role in the stability of an atom and can influence an element's physical properties and behavior. The difference in the number of neutrons can result in various isotopes having different nuclear reactions, such as different rates of decay or different interactions with other particles.

Mass Percent of Protons

The mass percent of protons in an isotope's nucleus can be found by dividing the number of protons by the mass number and then multiplying by 100 to get a percentage. For boron-10 and boron-11, the respective calculations yield 50% (\(\left( \frac{5}{10} \right) \times 100\% = 50\%\)) and approximately 45.45% (\(\left( \frac{5}{11} \right) \times 100\% \approx 45.45\%\)).

This mass percent helps to understand the composition of the nucleus in terms of its proton content, which is a defining factor for the identity of the element. Calculating the mass percent is significant when studying isotopic abundance and nuclear processes, as it contributes to the understanding of how mass is distributed within the nucleus of an atom.