Question

Determine the number of protons and the number of neutrons in each isotope. \begin{equation} \text { a. }\quad\frac{40}{19} \mathrm{K} \quad\quad\quad\quad \text { b. } \quad \frac{226}{88} \mathrm{Ra} \end{equation} \begin{equation} \text { c. }\quad 49 \mathrm{Tc} \quad \text { d. }\quad \frac{33}{15} \mathrm{P} \end{equation}

Short answer

a. 19 protons, 21 neutrons; b. 88 protons, 138 neutrons; c. 43 protons (Tc's atomic number), 6 neutrons; d. 15 protons, 18 neutrons.

Step-by-step solution

Identify the Atomic Number

The atomic number (Z) is the number located at the bottom of each isotope symbol and represents the number of protons. For each isotope provided, identify the atomic number.

Determine the Number of Protons

The number of protons in an atom is equal to the atomic number (Z). For each isotope, the number of protons is the same as Z.

Calculate the Number of Neutrons

To find the number of neutrons (N), subtract the atomic number (Z) from the mass number (A), which is the number at the top of the isotope symbol: N = A - Z. Do this for each isotope.

Key concepts

Atomic Number

The atomic number, often denoted by the symbol 'Z', is a fundamental concept in chemistry and physics. It refers to the number of protons found in the nucleus of an atom and is a unique identifier of a chemical element. For instance, every atom with 6 protons is carbon, and every atom with 8 protons is oxygen.
An important aspect of the atomic number is that it also tells us the number of electrons in a neutral atom—where the charges balance each other out. Having the same number of protons and electrons gives atoms their elemental properties and determines how they interact with other atoms in chemical reactions. For example, when students come across a symbol like \( \frac{40}{19} \mathrm{K} \), the atomic number is 19, indicating that potassium has 19 protons and, in its neutral state, 19 electrons.
Understanding the atomic number also helps to categorize elements in the periodic table, as elements are arranged in order of increasing atomic number, showcasing trends like reactivity or electronegativity that help predict the behavior of elements in different scenarios.

Number of Protons

Protons are positively charged subatomic particles found in the nucleus of an atom, and their quantity essentially defines the element's identity. The number of protons is equivalent to the atomic number 'Z' and remains constant for all atoms of an element. For instance, all hydrogen atoms have one proton, while all uranium atoms have 92 protons.
Because the number of protons determines the atomic number, which is crucial in organizing the periodic table, it is of paramount importance for students to comprehend that identifying the number of protons helps to pinpoint the element in question. The exercise presented shows isotopes with different mass numbers, such as \( \frac{226}{88} \mathrm{Ra} \), where despite the mass number being 226, the number of protons is the atomic number, 88, revealing the isotope to be of the element Radon.

Number of Neutrons

Neutrons are neutral subatomic particles found in the nucleus alongside protons. While they don't affect the chemical behavior of an element much, they are crucial for nuclear stability. The number of neutrons in an atom differs among isotopes, which are atoms of the same element that have varying numbers of neutrons.
To understand the number of neutrons in an isotope, students can use the formula 'N = A - Z', where 'A' is the mass number (the sum of protons and neutrons) and 'Z' is the atomic number (the number of protons). For example, Technetium (Tc) with a mass number of 49 has an atomic number of 43 (a property of all Tc atoms), indicating it has 43 protons. Using the formula, the number of neutrons is \( 49 - 43 = 6 \) neutrons. This difference in neutron number is what creates isotopes and can lead to different physical properties, such as stability or radioactive decay behavior, which are significant in fields like nuclear chemistry and medicine.