Question

How many protons, neutrons, and electrons are in the following atoms? (a) \({ }^{40} \mathrm{Ar}\), (b) \({ }^{65} \mathrm{Zn},(\mathbf{c}){ }^{70} \mathrm{Ga},(\mathbf{d}){ }^{80} \mathrm{Br},(\mathbf{e}){ }^{184} \mathrm{~W}\), (f) \({ }^{243} \mathrm{Am}\)

Short answer

(a) \( {}^{40}\mathrm{Ar} \): 18 protons, 22 neutrons, 18 electrons; (b) \( {}^{65}\mathrm{Zn} \): 30 protons, 35 neutrons, 30 electrons; (c) \( {}^{70}\mathrm{Ga} \): 31 protons, 39 neutrons, 31 electrons; (d) \( {}^{80}\mathrm{Br} \): 35 protons, 45 neutrons, 35 electrons; (e) \( {}^{184}\mathrm{W} \): 74 protons, 110 neutrons, 74 electrons; (f) \( {}^{243}\mathrm{Am} \): 95 protons, 148 neutrons, 95 electrons.

Step-by-step solution

(a) Argon (\( {}^{40}\mathrm{Ar} \))

For Argon (\( \mathrm{Ar} \)), the atomic number is 18. Therefore, it has 18 protons and 18 electrons. The atomic mass number is 40. To find the number of neutrons, we subtract the atomic number from the atomic mass number: \(40 - 18 = 22\). So Argon has 22 neutrons.

(b) Zinc (\( {}^{65}\mathrm{Zn} \))

For Zinc (\( \mathrm{Zn} \)), the atomic number is 30. Therefore, it has 30 protons and 30 electrons. The atomic mass number is 65. To find the number of neutrons, we subtract the atomic number from the atomic mass number: \(65 - 30 = 35\). So Zinc has 35 neutrons.

(c) Gallium (\( {}^{70}\mathrm{Ga} \))

For Gallium (\( \mathrm{Ga} \)), the atomic number is 31. Therefore, it has 31 protons and 31 electrons. The atomic mass number is 70. To find the number of neutrons, we subtract the atomic number from the atomic mass number: \(70 - 31 = 39\). So Gallium has 39 neutrons.

(d) Bromine (\( {}^{80}\mathrm{Br} \))

For Bromine (\( \mathrm{Br} \)), the atomic number is 35. Therefore, it has 35 protons and 35 electrons. The atomic mass number is 80. To find the number of neutrons, we subtract the atomic number from the atomic mass number: \(80 - 35 = 45\). So Bromine has 45 neutrons.

(e) Tungsten (\( {}^{184}\mathrm{W} \))

For Tungsten (\( \mathrm{W} \)), the atomic number is 74. Therefore, it has 74 protons and 74 electrons. The atomic mass number is 184. To find the number of neutrons, we subtract the atomic number from the atomic mass number: \(184 - 74 = 110\). So Tungsten has 110 neutrons.

(f) Americium (\( {}^{243}\mathrm{Am} \))

For Americium (\( \mathrm{Am} \)), the atomic number is 95. Therefore, it has 95 protons and 95 electrons. The atomic mass number is 243. To find the number of neutrons, we subtract the atomic number from the atomic mass number: \(243 - 95 = 148\). So Americium has 148 neutrons.

Key concepts

Atomic Number

The atomic number is a fundamental property of an element and one of the cornerstones of chemistry and physics. It is represented by the symbol 'Z' and uniquely identifies a chemical element. In essence, the atomic number tells us the number of protons present in the nucleus of an atom of the element.

Having a grasp of the atomic number is vital because it directly correlates to the element's position in the periodic table and defines its chemical behavior. For example, hydrogen has an atomic number of 1, corresponding to its single proton in the nucleus, distinguishing it from other elements.

When determining the number of electrons in a neutral atom (where no ionization has occurred), the atomic number also comes into play. A neutral atom has an equal number of protons and electrons. Therefore, if a carbon atom has an atomic number of 6, it also has 6 electrons orbiting its nucleus. As found in the textbook solution for Argon ({40}^{Ar}), with an atomic number of 18, it naturally contains 18 electrons in its neutral state.

Atomic Mass Number

The atomic mass number, denoted as 'A', is another crucial aspect of an atom's identity. It represents the total number of protons and neutrons in the atom's nucleus and is often regarded as the atom's 'weight'. The relationship between the atomic number (Z), atomic mass number (A), and the number of neutrons (N) in the nucleus is neatly summarized by the formula:$A\; =\; Z\; +\; N$This equation is straightforward to use: by simply rearranging it, we can find the number of neutrons by subtracting the atomic number from the atomic mass number (N = A - Z). This method is exactly what we see in the solutions provided for the elements like Zinc ({65}^{Zn}), with an atomic mass number of 65 and an atomic number of 30, giving us 35 neutrons after performing the subtraction.

Protons, Neutrons, Electrons

Atoms are made up of three fundamental particles: protons, neutrons, and electrons. Protons are positively charged particles found in the nucleus, and their number gives the atomic number of the element. Neutrons, found alongside protons in the nucleus, carry no charge and contribute to the mass of the atom without affecting its charge. Electrons are negatively charged and orbit the nucleus, balancing the positive charge of protons.

The number of protons and electrons usually matches in a neutral atom, which prevents the atom from having an overall electric charge. For example, as demonstrated in the Bromine ({80}^{Br}) example, there are 35 protons in the nucleus, and also 35 electrons orbiting the nucleus. This balance is crucial for the stability of an atom and the formation of chemical bonds.

It's essential to understand that while protons and electrons define the chemical identity and electrical balance of an atom, neutrons play a critical role in atomic stability. Elements can exist in various forms, known as isotopes, which have the same number of protons but different numbers of neutrons. Thus, understanding the interaction and numbers of protons, neutrons, and electrons is key to grasping basic atomic structure and the behavior of elements in the periodic table.