# Explanation About Electrons and Protons

Electrons and protons are fundamental particles that make up atoms, which are the basic building blocks of matter. Understanding their properties and interactions is key to the fields of chemistry and physics.

## Electrons

Electrons are subatomic particles with a negative electric charge. They are found in the electron cloud that surrounds the nucleus of an atom. Each electron carries a charge of -1 elementary charge, which is equivalent to approximately -1.602 x 10^-19 coulombs. Electrons have a very small mass; they are about 1/1836 the mass of a proton. In chemical reactions, electrons are often the particles that are exchanged or shared between atoms, leading to the formation of chemical bonds.

## Protons

Protons are positively charged subatomic particles located within the nucleus of an atom. They carry a positive electric charge equal in magnitude to the charge of an electron but of the opposite sign, +1 elementary charge or +1.602 x 10^-19 coulombs. Protons have a much larger mass than electrons, which contributes to the majority of the mass of an atom. The number of protons in the nucleus determines the element’s atomic number and defines the type of atom.

## Problems and Solutions About Electrons and Protons

Let’s explore some problems and solutions related to the properties of electrons and protons.

1. **Problem: Calculate the net charge of an ion with 10 protons and 8 electrons.**

**Solution:**

The net charge (Q) of an ion can be calculated using the formula:

$$ Q = (n_p – n_e) \cdot e $$

where \( n_p \) is the number of protons, \( n_e \) is the number of electrons, and \( e \) is the elementary charge (±1.602 x 10^-19 C).

For the given ion:

$$ Q = (10 – 8) \cdot (+1.602 \times 10^{-19} \text{ C}) $$

$$ Q = 2 \cdot 1.602 \times 10^{-19} \text{ C} $$

$$ Q = 3.204 \times 10^{-19} \text{ C} $$

The ion has a net positive charge of 3.204 x 10^-19 coulombs.

2. **Problem: An atom has 15 protons. How many electrons must it have to be electrically neutral?**

**Solution:**

For an atom to be electrically neutral, the number of protons must equal the number of electrons. Since the atom has 15 protons, it must also have 15 electrons to be neutral.

3. **Problem: If a proton and electron are 1.0 x 10^-10 meters apart, what is the force of attraction between them?**

**Solution:**

The force between the two charges can be calculated by Coulomb’s Law:

$$ F = k \frac{|q_1 q_2|}{r^2} $$

where \( k \) is Coulomb’s constant (\( 8.9875 \times 10^9 \text{ Nm}^2/\text{C}^2 \)), \( q_1 \) and \( q_2 \) are the charges of the proton and electron respectively, and \( r \) is the distance between them.

Here we have:

$$ F = 8.9875 \times 10^9 \frac{(1.602 \times 10^{-19} \text{ C})^2}{(1.0 \times 10^{-10} \text{ m})^2} $$

$$ F = 8.9875 \times 10^9 \frac{(2.56 \times 10^{-38} \text{ C}^2)}{1.0 \times 10^{-20} \text{ m}^2} $$

$$ F = 8.9875 \times 10^9 \times 2.56 \times 10^{-18} \text{ N} $$

$$ F \approx 2.3 \times 10^{-8} \text{ N} $$

The force of attraction between them is approximately \( 2.3 \times 10^{-8} \) newtons.

4. **Problem: What is the mass difference between a proton and an electron?**

**Solution:**

The mass of a proton is approximately \( 1.6726 \times 10^{-27} \) kilograms, and the mass of an electron is approximately \( 9.1094 \times 10^{-31} \) kilograms.

The mass difference is:

$$ \Delta m = m_{\text{proton}} – m_{\text{electron}} $$

$$ \Delta m = 1.6726 \times 10^{-27} \text{ kg} – 9.1094 \times 10^{-31} \text{ kg} $$

$$ \Delta m \approx 1.6726 \times 10^{-27} \text{ kg} $$

The mass difference is approximately \( 1.6726 \times 10^{-27} \) kilograms since the mass of the electron is negligible compared to that of the proton.

5. **Problem: An atom has 2 more protons than electrons. What is the net charge of the atom?**

**Solution:**

If the atom has 2 more protons (n_p) than electrons (n_e), then \( n_p = n_e + 2 \).

The net charge (Q) of the atom is:

$$ Q = (n_p – n_e) \cdot e $$

$$ Q = 2 \cdot 1.602 \times 10^{-19} \text{ C} $$

$$ Q = 3.204 \times 10^{-19} \text{ C} $$

The atom has a net positive charge of \( 3.204 \times 10^{-19} \) coulombs.

6. **Problem: How many protons are there in a neutral atom with an atomic mass of 40 and 20 neutrons?**

**Solution:**

A neutral atom has an equal number of protons and electrons. The atomic mass is roughly the sum of the number of protons (p) and neutrons (n). Therefore, if there are 20 neutrons:

$$ p + n = \text{Atomic Mass} $$

$$ p + 20 = 40 $$

$$ p = 40 – 20 $$

$$ p = 20 $$