a) Two protons in a molecule are 3.80 multiplied by 10-10 m apart. Find the electrical force exerted by one proton on the other.
Magnitude
N
(b) State how the magnitude of this force compares with the magnitude of the gravitational force exerted by one proton on the other.
(electrical force / gravitational force)
(c) What if? What must be a particle's charge-to-mass ratio if the magnitude of the gravitational force between two of these particles is equal to the magnitude of electrical force between them?
C/k
how to calculate this question
To find the electrical force exerted by one proton on the other, you can use Coulomb's law equation:
F = ke * (q1 * q2) / r^2
where F is the electrical force, ke is the electrostatic constant (approximately 8.99 x 10^9 Nm^2/C^2), q1 and q2 are the charges of the protons (both equal to the elementary charge, approximately 1.6 x 10^-19 C), and r is the distance between the protons (3.80 x 10^-10 m).
(a) Plugging in the values, we can calculate the magnitude of the electrical force:
F = (8.99 x 10^9 Nm^2/C^2) * [(1.6 x 10^-19 C) * (1.6 x 10^-19 C)] / (3.80 x 10^-10 m)^2
Simplifying this equation will give you the magnitude of the electrical force in newtons (N).
(b) To compare the magnitude of the electrical force with the magnitude of the gravitational force between the two protons, we can use the formula:
(Electrical force / Gravitational force) = (ke * (q1 * q2) / r^2) / (G * (m1 * m2) / r^2)
where G is the gravitational constant (approximately 6.67 x 10^-11 Nm^2/kg^2), m1 and m2 are the masses of the protons (approximately 1.67 x 10^-27 kg), and r is the distance between the protons.
By substituting the values, you can calculate the ratio of the electrical force to the gravitational force.
(c) For the magnitude of the gravitational force to be equal to the magnitude of the electrical force between the two particles, you can equate the two equations:
ke * (q1 * q2) / r^2 = G * (m1 * m2) / r^2
Since the distance r is the same for both forces and cancels out, you are left with:
(q1 * q2) / (m1 * m2) = G / ke
Solving for the charge-to-mass ratio, you get:
C/k = (q1 * q2) / (m1 * m2)
So, the charge-to-mass ratio of the particle must be equal to (q1 * q2) / (m1 * m2) in C/kg for the magnitude of the gravitational force to be equal to the magnitude of the electrical force.