Find the force (in N) of electrical attraction between a proton and an electron that are 8.5 ✕ 10−11 m apart.
______ N
Compare this to the gravitational force between these particles. (Enter the gravitational force, in N.)
______ N
To find the force of electrical attraction between a proton and an electron, we can use Coulomb's Law:
F = k * (|q1*q2|) / r^2
Where:
F = force of electrical attraction
k = Coulomb's constant = 8.99 x 10^9 N m^2/C^2
q1 = charge of proton = 1.6 x 10^-19 C
q2 = charge of electron = -1.6 x 10^-19 C (since electrons have a negative charge)
r = distance between the particles = 8.5 x 10^-11 m
Plugging in the values:
F = (8.99 x 10^9) * (|1.6 x 10^-19 * -1.6 x 10^-19|) / (8.5 x 10^-11)^2
F = (8.99 x 10^9) * (2.56 x 10^-38) / (7.225 x 10^-21)
F = 3.21 x 10^-28 N
So, the force of electrical attraction between a proton and an electron that are 8.5 x 10^-11 m apart is 3.21 x 10^-28 N.
Next, to find the gravitational force between these particles, we can use Newton's Law of Universal Gravitation:
F = G * (m1*m2) / r^2
Where:
F = gravitational force
G = gravitational constant = 6.67 x 10^-11 N m^2/kg^2
m1 = mass of proton = 1.67 x 10^-27 kg
m2 = mass of electron = 9.11 x 10^-31 kg (mass of an electron is approximately 1/1836 times the mass of a proton)
r = distance between the particles = 8.5 x 10^-11 m
Plugging in the values:
F = (6.67 x 10^-11) * (1.67 x 10^-27 * 9.11 x 10^-31) / (8.5 x 10^-11)^2
F = (6.67 x 10^-11) * (1.52 x 10^-57) / (7.225 x 10^-21)
F = 1.40 x 10^-67 N
So, the gravitational force between a proton and an electron that are 8.5 x 10^-11 m apart is 1.40 x 10^-67 N.
Therefore, the force of electrical attraction between the particles is much stronger than the gravitational force between them.