Atoms consist of particles, which contain an electrical charge and mass, both of which, however, are extremely small. The ratio of mass to charge is known as the specific charge of the atom.
Atoms and their charge
Atoms are neutral; they have no charge because their particles are balanced. However, if you remove or add one of their negative charges (electrons), you have a non-balanced atom. An atom or particle with a charge other than zero is called an ion. Ions can be positive (cation) or negative (anion).
- Cation: a positively charged ion, which has an excess of positive particles.
- Anion: a negatively charged ion, which has an excess of negative particles.
Fig. 1 - From left to right: a hydrogen anion, a neutral hydrogen atom, and a Hydrogen cation
The specific charge of electrons and protons
Not only atoms can have a specific charge; the same is true of elemental particles. The specific charge of each particle depends on the particle’s mass and charge (see below), which also affects the specific charge of the atom.
- The magnitude of the specific charge of electrons is larger than the specific charge of protons because the proton is heavier than the electron.
- The neutron has a specific charge of zero, as it has a neutral charge.
- In an atom with an equal number of protons and electrons, the specific charge is zero.
How to calculate the specific charge of a particle
To obtain the specific charge of a particle, we need to know its mass and electrical charge. Based on these, we can calculate the specific charge by dividing a particle’s electrical charge by its mass:
\[\text{Specific charge} = \frac{\text{Electrical Charge}}{\text{Particle Mass}}\]
The mass and charge of an atom are shown in the nuclide notation, which determines the number of particles that make up the mass of the nucleus and the total number of protons in an element’s single atom.
Reading the nuclide notation
The nuclide notation tells us the element symbol (in Latin letters) and part of the atom’s structure, using its mass number and atomic number:
- The mass number, which indicates the number of protons and neutrons that make up the element’s mass, is in the upper left corner.
- The atomic number in the lower-left corner shows the number of protons in the atom.
See the two examples below.
\(^{12}_{6}C\)
The symbol tells us that we are dealing with a carbon atom, with the number twelve indicating that Carbon 12 has twelve particles in its nucleus.
The particles in the nucleus make up most of the atom’s mass. The number six gives us the number of positive charges (or protons) in the nucleus.
\(^{16}_{8}O\)
The symbol tells us that we are dealing with an oxygen atom, with the number sixteen indicating that Oxygen 16 has sixteen particles in its nucleus.
The number eight gives us the number of positive charges in the nucleus.
Fig. 2 - The nuclide notation contains information about the atom's structure
Obtaining the electrical charge
To obtain the electrical charge, we need to multiply the number of charged particles by the charge value, as illustrated in the following examples.
Calculate the total charge of a helium nucleus.
\(^{4}_{2}He\)
We need to multiply the charge of one proton by the total number of protons in the nucleus. The proton charge is equal to \(1.6022 \cdot 10 ^ {-19}\) coulombs, so we need to multiply the total number of helium protons, which is two, by the charge value.
\(\text{Total charge} = 2 \cdot (1.6022 \cdot 10^{-19} C) = 3.2044 \cdot 10^{-19} C\)
Calculate the total charge of a carbon anion with eight electrons.
An anion is a negatively charged atom. A carbon atom normally has six electrons, but in this case, we are dealing with an atom that has two extra electrons and thus a total of eight. These additional electrons give the atom a negative total charge.
To obtain the total charge, we need to multiply the electron charge value by the extra electrons. The electron charge is \(-1.6022 \cdot 10 ^{-19}\) coulombs. The total charge, therefore, is \(-1.6022 \cdot 10 ^{-19}\) coulombs multiplied by two.
\(\text{Total charge} = 2 \cdot (-1.6022 \cdot 10^{-19} C) = -3.2044 \cdot 10^{-19} C\)
As you can see from these examples, the charge magnitude of an electron and a proton are the same. The only difference between them is the minus sign.
To obtain the number of protons in the nucleus without having the nuclide notation, you need to consult the periodic table of elements. The atomic number tells you the number of protons in the atom’s nucleus.
Obtaining the mass
To obtain the total particle mass, we need to multiply the mass value of protons and neutrons by the number of protons and neutrons in the atom. The electron’s mass is so small that we don’t need to calculate it. The approximate mass of both protons and neutrons is \(1.67 \cdot 10 ^ {-27}kg\), although neutrons are slightly heavier.
Obtaining the specific charge
After we have obtained the total charge and the total mass of the particle, we only need to divide the total charge by the total mass, as in the following example.
Calculate the specific charge of a nucleus of Carbon 12.
\(^{12}_{6}C\)
To calculate the specific charge, we first multiply the charge of one proton by the total number of protons, which in the case of a carbon atom is six.
\(\text{Total charge} = 6 \cdot (1.6022 \cdot 10^{-19} C) = 9.6132 \cdot 10^{-19} C\)
Now we multiply the mass of the particles that make up the nucleus by the particle’s number, which in this case is twelve.
\(\text{Total charge} = 12 \cdot (1.67 \cdot 10^{-27} kg) = 20.04 \cdot 10^{-27} kg\)
Finally, you need to divide the two quantities.
\(\text{Specific charge} = \frac{\text{Electrical charge}}{\text{Particle mass}} = 4.79701 \cdot 10^7 \space C/kg\)
Specific Charge - Key takeaways
- The specific charge of an atom is the ratio of its electrical charge to its mass.
- The magnitude of the electrical charge of both electrons and protons is the same, but that of electrons is negative.
- The mass of electrons is smaller than that of protons and neutrons.
- A positively charged particle is called a cation, while a negatively charged particle is called an anion.
- Neutrons do not add any charge to the atom; they only add mass.
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