The hydrogen atom contains a proton, mass 1.67 10-27 kg, and an electron, mass 9.11 10-31 kg. The average distance between them is 5.3 10-11 m. The charge of the proton is the same size, opposite sign of the electron.
a)What is the magnitude of the average electrostatic attraction between them?
F=kqq/d^2
You would have to convert from kg to C, correct? Then, plug everything into the formula.
b)What is the magnitude of the average gravitational attraction between them?
I am drawing a complete blank on the formula for this one and I cannot find it in my notes.
a) To find the magnitude of the average electrostatic attraction between the proton and the electron, we can use the formula:
F = k * q1 * q2 / d^2
Where:
F = Force of electrostatic attraction
k = electrostatic constant (8.99 x 10^9 Nm^2/C^2)
q1 = charge of proton (in C)
q2 = charge of electron (in C)
d = distance between them (in m)
Since the charge of the proton and electron are equal in magnitude and opposite in sign, we can consider them to be +e and -e respectively, where e = 1.6 x 10^-19 C.
Plugging in the values:
F = (8.99 x 10^9 Nm^2/C^2) * (1.6 x 10^-19 C) * (1.6 x 10^-19 C) / (5.3 x 10^-11 m)^2
b) To find the magnitude of the average gravitational attraction between the proton and the electron, we can use the formula:
F = G * (m1 * m2) / d^2
Where:
F = Force of gravitational attraction
G = gravitational constant (6.67 x 10^-11 Nm^2/kg^2)
m1 = mass of the proton (in kg)
m2 = mass of the electron (in kg)
d = distance between them (in m)
Plugging in the values:
F = (6.67 x 10^-11 Nm^2/kg^2) * (1.67 x 10^-27 kg) * (9.11 x 10^-31 kg) / (5.3 x 10^-11 m)^2
Please note that the gravitational force is extremely weak compared to the electrostatic force in this case.
a) To find the magnitude of the average electrostatic attraction between the proton and electron, you need to use Coulomb's Law, which states that the force of attraction between two charged objects is given by:
F = (k * q1 * q2) / d^2
where:
- F is the electrostatic force
- k is Coulomb's constant (which is approximately 9 x 10^9 Nm²/C²)
- q1 and q2 are the charges of the proton and electron, respectively
- d is the distance between them
Since the charge of the proton is the same size as the electron but with the opposite sign, we can use the charge value (1.6 x 10^-19 C) for both q1 and q2 in magnitude.
So, plugging the values into the formula:
F = (9 x 10^9 Nm²/C²) * (1.6 x 10^-19 C) * (1.6 x 10^-19 C) / (5.3 x 10^-11 m)^2
Calculating this expression will give you the magnitude of the average electrostatic attraction between the proton and electron.
b) The formula for the magnitude of the average gravitational attraction between two objects is given by Newton's Law of Universal Gravitation:
F = (G * m1 * m2) / d^2
where:
- F is the gravitational force
- G is the gravitational constant (approximately 6.6743 x 10^-11 Nm²/kg²)
- m1 and m2 are the masses of the objects
- d is the distance between them
In this case, we are considering the gravitational attraction between the proton and electron. However, the gravitational force between them is negligible because the mass of the electron is much smaller compared to the mass of the proton. Therefore, you can assume that the gravitational force is essentially zero.
Hence, the magnitude of the average gravitational attraction between them is practically zero.
There are some mistakes in the problem. The average distance between the electron and the proton is not equal to 5.3 10^(-11) m. The distance
a = 5.3 10^(-11) m is the Bohr radius which and at this distance is the most likely distance for the electron to be.
The average distance is 3/2 a. In this problem you need to know the average of 1/d^2, which is given by 2/a^2. So, you need to find the charge of the electron, e, anbd evaluate:
2 k e^2/a^2
The average gravitational attraction is given by:
2 G m^2/a^2
Of course, the other mistake in this problem is that it is suggested that the average attractive force would be given by k e^2/a^2 :)