The mass of an electron is 9.11*10-31kg,that of a proton of mass is 1.67*10^-27kg.find the ratio of Fe/Fg of the electric feild and gravitional feild exerted by electron and proton

To find the ratio of the electric field force (F_e) to the gravitational field force (F_g) exerted by an electron and a proton, we need to use the formulas for both forces. The electric force between two charged particles is given by Coulomb's law, while the gravitational force is described by Newton's law of universal gravitation. Let's break this down step by step.

Understanding the Forces

The electric force (F_e) between two charges can be calculated using the formula:

F_e = k * |q1 * q2| / r²

Where:

• k is Coulomb's constant, approximately 8.99 x 10^9 N m²/C².
• q1 and q2 are the charges of the particles.
• r is the distance between the charges.

The gravitational force (F_g) is calculated using:

F_g = G * (m1 * m2) / r²

Where:

• G is the gravitational constant, approximately 6.67 x 10^-11 N m²/kg².
• m1 and m2 are the masses of the particles.
• r is the distance between the masses.

Calculating the Forces

For our scenario, we will consider the electron and proton as point charges and masses. The charge of an electron (q_e) is approximately -1.6 x 10^-19 C, and the charge of a proton (q_p) is approximately +1.6 x 10^-19 C. The masses are:

• Mass of electron (m_e) = 9.11 x 10^-31 kg
• Mass of proton (m_p) = 1.67 x 10^-27 kg

Now, let's calculate the ratio of the electric force to the gravitational force:

Finding the Ratio F_e / F_g

We can express the ratio as:

F_e / F_g = (k * |q_e * q_p| / r²) / (G * (m_e * m_p) / r²)

Notice that the r² cancels out:

F_e / F_g = (k * |q_e * q_p|) / (G * (m_e * m_p))

Plugging in the Values

Substituting the known values:

• k = 8.99 x 10^9 N m²/C²
• G = 6.67 x 10^-11 N m²/kg²
• |q_e * q_p| = (1.6 x 10^-19 C)² = 2.56 x 10^-38 C²
• m_e * m_p = (9.11 x 10^-31 kg) * (1.67 x 10^-27 kg) = 1.52 x 10^-57 kg²

Now, substituting these values into the ratio:

F_e / F_g = (8.99 x 10^9 * 2.56 x 10^-38) / (6.67 x 10^-11 * 1.52 x 10^-57)

Calculating the numerator:

Numerator = 8.99 x 10^9 * 2.56 x 10^-38 = 2.30 x 10^-28

Calculating the denominator:

Denominator = 6.67 x 10^-11 * 1.52 x 10^-57 = 1.01 x 10^-67

Now, dividing the numerator by the denominator:

F_e / F_g = 2.30 x 10^-28 / 1.01 x 10^-67 = 2.28 x 10^39

Final Result

The ratio of the electric field force to the gravitational field force exerted by an electron and a proton is approximately 2.28 x 10^39. This indicates that the electric force is vastly stronger than the gravitational force at the scale of subatomic particles.