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/kg
To find the electrical force exerted by one proton on the other, we can use Coulomb's Law, which states that the magnitude of the electrical force between two charged particles is given by:
F = k * (q1 * q2) / r^2
where F is the force, k is the electrostatic constant (9 x 10^9 N m^2/C^2), q1 and q2 are the charges of the two objects, and r is the distance between the charges.
In this case, we have two protons, which both have a charge of +e, where e is the elementary charge (1.6 x 10^(-19) C). The distance between them (r) is given as 3.80 x 10^(-10) m.
So, plugging in the values into the formula, we can calculate the electrical force exerted by one proton on the other:
F = (9 x 10^9 N m^2/C^2) * ((+e) * (+e)) / (3.80 x 10^(-10) m)^2
Calculating the above expression will give us the magnitude of the electrical force in Newtons.
(b) To compare the magnitude of the electrical force with the gravitational force exerted by one proton on the other, we can calculate the ratio of the electrical force to the gravitational force:
(electrical force / gravitational force)
The gravitational force between two objects can be calculated using the formula:
F_gravity = G * (m1 * m2) / r^2
where F_gravity is the gravitational force, G is the gravitational constant (6.67 x 10^(-11) N m^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between them.
For two protons, we can assume their mass is equal to each other, so m1 = m2 = mp (the mass of a proton, approximately 1.67 x 10^(-27) kg).
To compare the magnitudes, we can find the ratio of the electrical force to the gravitational force by dividing the electrical force value calculated in part (a) by the gravitational force value calculated using the formula above.
(c) If we want the magnitude of the gravitational force to be equal to the magnitude of the electrical force between two particles, we can set the two forces equal to each other and solve for the charge-to-mass ratio.
(F_gravity) = (F_electrical)
(G * (m1 * m2) / r^2) = (k * (q1 * q2) / r^2)
Since m1 = m2, we can simplify the equation to:
G * (m^2) / r^2 = k * (q^2) / r^2
Simplifying further, we get:
G * m^2 = k * q^2
Now, we can solve for the charge-to-mass ratio (q/m) by dividing both sides of the equation by (m^2):
(q/m)^2 = (G * m^2) / k
Taking the square root of both sides:
q/m = √((G * m^2) / k)
Solving this equation will give us the required charge-to-mass ratio (in C/kg).