A proton and an electron in a hydrogen atom are separated by a distance of 5.3 x 10-11 m. The magnitude and direction of electric field set up by the proton at the position of the electron is:
a. 5.1 x1011 N/C away from the proton
b. 5.1 x1011 N/C toward the proton
c. 5.1 x1010 N/C toward the proton
d. 5.1 x1010 N/C away from the proton
Well, let me tell you a shocking answer! The correct answer is:
b. 5.1 x 10^11 N/C toward the proton.
That proton really knows how to pull in some positive energy!
To find the magnitude and direction of the electric field set up by the proton at the position of the electron in a hydrogen atom, we can use Coulomb's law.
Coulomb's law states that the electric field at a point due to a point charge is given by the equation:
E = k * (q / r^2)
Where E is the electric field, k is Coulomb's constant (8.99 x 10^9 N m^2/C^2), q is the charge, and r is the distance between the charges.
In this case, the proton has a charge of +1.6 x 10^-19 C, the electron has a charge of -1.6 x 10^-19 C, and the distance between them is 5.3 x 10^-11 m.
Plugging in the values, we get:
E = (8.99 x 10^9 N m^2/C^2) * (1.6 x 10^-19 C / (5.3 x 10^-11 m)^2)
Simplifying the equation, we have:
E ≈ 5.1 x 10^10 N/C
So, the magnitude of the electric field set up by the proton at the position of the electron is approximately 5.1 x 10^10 N/C. Now, let's determine the direction of the electric field.
Since the proton has a positive charge and the electron has a negative charge, the electric field will point from the proton towards the electron.
Therefore, the correct answer is:
c. 5.1 x 10^10 N/C toward the proton
To find the magnitude and direction of the electric field set up by the proton at the position of the electron, we can use Coulomb's Law.
Coulomb's Law states that the electric field created by a point charge is given by the equation:
E = k * (Q / r^2)
Where:
E is the electric field
k is the electrostatic constant (k = 9 x 10^9 N*m^2/C^2)
Q is the charge of the point charge
r is the distance from the point charge
In this case, the point charge is the proton, which has a charge of +1.6 x 10^-19 C. The distance between the proton and the electron is given as 5.3 x 10^-11 m.
Plugging the values into the equation, we have:
E = (9 x 10^9 N*m^2/C^2) * (1.6 x 10^-19 C) / (5.3 x 10^-11 m)^2
Evaluating this expression, we find that:
E ≈ 5.1 x 10^11 N/C
The electric field is directed from positive charges to negative charges. In this case, the proton is positive and the electron is negative, so the electric field points from the proton towards the electron.
Therefore, the correct answer is: b. 5.1 x 10^11 N/C toward the proton.