Suppose that 7.40 g of hydrogen is separated into electrons and protons. Suppose also that the protons are placed at the Earth's north pole and the electrons are placed at the south pole. What is the resulting compressional force on the Earth?
F = kq1q2/r^2
Have to find how many protons and electrons in .0074 kg of H2 and the radius of the Earth. Charge on each proton/electron is 1.6e-19 C.
To calculate the resulting compressional force on the Earth due to the separation of protons and electrons, we need to consider the electric force between them.
Here are the steps to calculate the compressional force:
1. Determine the number of protons and electrons: The question states that 7.40 g of hydrogen is separated into protons and electrons. Since the atomic mass of hydrogen is 1 g/mol, we can convert the mass of hydrogen to moles. Using the molar mass of hydrogen (1 g/mol), we find that there are 7.40 moles of hydrogen. Since one hydrogen atom consists of one proton and one electron, the number of protons and electrons is also 7.40 moles.
2. Calculate the total charge: Each proton has a charge of +1 elementary charge (e) and each electron has a charge of -1 e. The elementary charge is approximately 1.602 x 10^-19 C. Therefore, the total charge is calculated by multiplying the number of elementary charges by the charge of one elementary charge. In this case, the total charge is (7.40 moles x 6.022 x 10^23 particles/mole) x (1.602 x 10^-19 C/elementary charge).
3. Calculate the electric force: The electric force between two charged particles can be calculated using Coulomb's Law. The formula for the magnitude of the electric force (F) between two charges (q1 and q2) separated by a distance (r) is given by:
F = k * |q1 * q2| / r^2,
where k is the electrostatic constant (approximately 8.988 x 10^9 N m^2 C^-2).
In this case, the charges are the protons and electrons, and the distance between them is the radius of the Earth (approximately 6.371 x 10^6 m). Since the charges have opposite signs, the force will be attractive.
4. Substitute the values into the formula: Substitute the value of the charge calculated in step 2 for q1 and q2, and the value of the Earth's radius for r, into the Coulomb's Law formula.
5. Calculate the compressional force: The compressional force is the force experienced by Earth due to the separation of charges. Since the electrons are placed at the south pole and the protons at the north pole, the force will be directed vertically towards the center of the Earth. Take the negative of the magnitude of the electric force to represent the compression.
Following these steps will allow us to find the resulting compressional force on the Earth.