Question

What number of protons and neutrons is contained in the nucleus of each of the following atoms? Assuming each atom is uncharged, what number of electrons is present? a. \(\frac{235}{92} \mathrm{U}\) b. \(_{13}^{2} \mathrm{Al}\) c. \(\frac{57}{26} \mathrm{Fe}\) d. \(\frac{208}{82} \mathrm{Pb}\) e. \(\frac{86}{32} \mathrm{Rb}\) f. \(\frac{41}{20} \mathrm{Ca}\)

Short answer

a. Uranium (\(\frac{235}{92} U\)): 92 protons, 143 neutrons, 92 electrons b. Aluminum (\(_{13}^{27} Al\)): 13 protons, 14 neutrons, 13 electrons c. Iron (\(\frac{57}{26} Fe\)): 26 protons, 31 neutrons, 26 electrons d. Lead (\(\frac{208}{82} Pb\)): 82 protons, 126 neutrons, 82 electrons e. Rubidium (\(\frac{86}{37} Rb\)): 37 protons, 49 neutrons, 37 electrons f. Calcium (\(\frac{41}{20} Ca\)): 20 protons, 20 neutrons, 20 electrons

Step-by-step solution

a. Uranium (\(\frac{235}{92} \mathrm{U}\))

For Uranium (U), the atomic number is 92 and the mass number is 235. 1. Find the number of protons: The atomic number is 92, so Uranium has 92 protons. 2. Find the number of neutrons: The mass number is 235, so subtract the atomic number (protons) from the mass number: 235 - 92 = 143. Uranium has 143 neutrons. 3. Find the number of electrons: Since it's uncharged, the number of electrons equals the number of protons, 92 electrons.

b. Aluminum (\(_{13}^{27} \mathrm{Al}\))

For Aluminum (Al), the atomic number is 13 and the mass number is 27. 1. Find the number of protons: The atomic number is 13, so Aluminum has 13 protons. 2. Find the number of neutrons: Subtract the atomic number (protons) from the mass number: 27 - 13 = 14. Aluminum has 14 neutrons. 3. Find the number of electrons: Since it's uncharged, the number of electrons equals the number of protons, 13 electrons.

c. Iron (\(\frac{57}{26} \mathrm{Fe}\))

For Iron (Fe), the atomic number is 26 and the mass number is 57. 1. Find the number of protons: The atomic number is 26, so Iron has 26 protons. 2. Find the number of neutrons: Subtract the atomic number (protons) from the mass number: 57 - 26 = 31. Iron has 31 neutrons. 3. Find the number of electrons: Since it's uncharged, the number of electrons equals the number of protons, 26 electrons.

d. Lead (\(\frac{208}{82} \mathrm{Pb}\))

For Lead (Pb), the atomic number is 82 and the mass number is 208. 1. Find the number of protons: The atomic number is 82, so Lead has 82 protons. 2. Find the number of neutrons: Subtract the atomic number (protons) from the mass number: 208 - 82 = 126. Lead has 126 neutrons. 3. Find the number of electrons: Since it's uncharged, the number of electrons equals the number of protons, 82 electrons.

e. Rubidium (\(\frac{86}{37} \mathrm{Rb}\))

For Rubidium (Rb), the atomic number is 37 and the mass number is 86. 1. Find the number of protons: The atomic number is 37, so Rubidium has 37 protons. 2. Find the number of neutrons: Subtract the atomic number (protons) from the mass number: 86 - 37 = 49. Rubidium has 49 neutrons. 3. Find the number of electrons: Since it's uncharged, the number of electrons equals the number of protons, 37 electrons.

f. Calcium (\(\frac{41}{20} \mathrm{Ca}\))

For Calcium (Ca), the atomic number is 20 and the mass number is 40. 1. Find the number of protons: The atomic number is 20, so Calcium has 20 protons. 2. Find the number of neutrons: Subtract the atomic number (protons) from the mass number: 40 - 20 = 20. Calcium has 20 neutrons. 3. Find the number of electrons: Since it's uncharged, the number of electrons equals the number of protons, 20 electrons.

Key concepts

Atomic Number

The atomic number is a fundamental characteristic of an element and represents the number of protons found in the nucleus of an atom. This number not only determines the identity of the element but also its position on the periodic table. For example, the element Uranium (U) has an atomic number of 92, indicating that a Uranium atom contains 92 protons. In an uncharged atom, the atomic number also gives the number of electrons, since the positive charge of protons is balanced by the equal number of negatively charged electrons.

Knowing the atomic number is essential for discerning between different elements and predicting their chemical properties. Elements are organized in the periodic table in ascending order based on their atomic numbers, which helps in further understanding their systematic behavior.

Atomic Mass Number

The atomic mass number, also referred to as the atomic mass, is the total count of protons and neutrons in the atom's nucleus. Unlike the atomic number, the atomic mass number isn't as straightforward in determining an element’s characteristics. For example, Iron (Fe) has a mass number of 57, which is the sum of its 26 protons and 31 neutrons. This number is crucial when understanding isotopes, which are atoms of the same element (same atomic number) but with different numbers of neutrons, thus leading to a different atomic mass number.

The mass number helps in calculating an atom’s weight and it is typically found as the larger number located at the top left corner of the element's symbol when represented in a nuclear symbol.

Counting Protons and Neutrons

To determine the number of protons in an atom, one simply identifies the atomic number of that particular element. When it comes to counting neutrons, subtract the atomic number from the atomic mass number. For the element Lead (Pb), with an atomic mass number of 208 and an atomic number of 82, the calculation 208 - 82 reveals that Lead has 126 neutrons. It's crucial to master these calculations as they are fundamental to understanding the atomic nucleus and help to predict isotopic masses and nuclear stability.

Uncharged Atoms

Uncharged atoms, or neutral atoms, possess an equal number of protons and electrons, leading to no overall net charge. Each positively charged proton is balanced by a negatively charged electron. In an uncharged Rubidium (Rb) atom, for instance, there are 37 protons and, consequently, 37 electrons. This balance is what typically exists in nature for most elements unless they lose or gain electrons to become ions through chemical reactions or other means. Recognizing the state of an atom - whether charged or uncharged - is a key step in predicting how an atom will interact with others.

Atomic Structure

Atomic structure denotes the arrangement of particles within an atom, which includes a central nucleus surrounded by electrons in various energy levels. The nucleus contains the protons with a positive charge and neutrons with no charge. The electrons are located in orbitals outside the nucleus. The way these subatomic particles are organized influences the atom's chemical behavior and its interaction with other atoms.

For instance, the atomic structure dictates how atoms create bonds, their reactivity, and their placement in the periodic table. The variety in the atomic structures across different elements leads to the richness of chemical compounds we observe in the universe. A detailed understanding of atomic structure is essential for anyone venturing into the fields of chemistry, physics, and material sciences.