The mass of an electron is 9.109×10−31 kg, and the magnitude of the charge of an electron is 1.602×10−19 C. What is the ratio of the gravitational force to the electrostatic force between two electrons?
3.093×10^22
4.165×10^42
3.233×10^−23
2.390×10^−43
Can someone please help, i'm so confused.
the answer is 2.390 x 10^-43
To find the ratio of the gravitational force to the electrostatic force between two electrons, we can use the following formulas:
Gravitational force (Fg) between two objects: Fg = (G * m1 * m2) / r^2
Electrostatic force (Fe) between two charges: Fe = (k * q1 * q2) / r^2
Where:
G = gravitational constant
m1 = mass of the first object/particle
m2 = mass of the second object/particle
r = distance between the two objects/particles
k = Coulomb constant (electrostatic constant)
q1 = charge of the first object/particle
q2 = charge of the second object/particle
Given:
Mass of an electron (m) = 9.109×10^−31 kg
Charge of an electron (q) = 1.602×10^−19 C
First, we need to find the gravitational constant (G) and the Coulomb constant (k):
G = 6.67430 × 10^−11 N m^2/kg^2
k = 8.9875517923 × 10^9 N m^2/C^2
Now, we need to calculate the ratio of the forces:
Fg / Fe = ((G * m * m) / r^2) / ((k * q * q) / r^2)
Fg / Fe = (G * m * m) / (k * q * q)
Substituting the given values:
Fg / Fe = (6.67430 × 10^−11 N m^2/kg^2) * (9.109×10^−31 kg) * (9.109×10^−31 kg) / (8.9875517923 × 10^9 N m^2/C^2) * (1.602×10^−19 C) * (1.602×10^−19 C)
Performing the calculations:
Fg / Fe ≈ 2.39 × 10^−43
Hence, the ratio of the gravitational force to the electrostatic force between two electrons is approximately 2.39 x 10^−43.
Therefore, the correct option is 2.390×10^−43.
Sure! I can help you with that.
To determine the ratio of the gravitational force to the electrostatic force between two electrons, we need to calculate both forces and then divide them.
The gravitational force between two objects can be calculated using the formula:
F_grav = (G * m1 * m2) / r^2
Where:
- F_grav is the gravitational force between the two objects
- G is the gravitational constant (approximately 6.674 × 10^−11 N m^2 kg^−2)
- m1 and m2 are the masses of the two objects
- r is the distance between the centers of the two objects
In this case, the two objects are electrons, so we can use the mass of an electron (9.109×10−31 kg) for both m1 and m2.
The electrostatic force between two charged objects can be calculated using Coulomb's law:
F_el = (k * |q1 * q2|) / r^2
Where:
- F_el is the electrostatic force between the two objects
- k is the electrostatic constant (approximately 8.987 × 10^9 N m^2 C^−2)
- q1 and q2 are the charges of the two objects
- r is the distance between the centers of the two objects
In this case, the charges of the two electrons are equal and opposite, so we can use the magnitude of the charge of an electron (1.602×10−19 C) for both q1 and q2.
Now, let's substitute the values into the equations and calculate the forces:
F_grav = (6.674 × 10^−11 N m^2 kg^−2) * (9.109×10−31 kg) * (9.109×10−31 kg) / r^2
F_el = (8.987 × 10^9 N m^2 C^−2) * (1.602×10−19 C) * (1.602×10−19 C) / r^2
To find the ratio, divide the gravitational force by the electrostatic force:
Ratio = F_grav / F_el
Now you can substitute the values and calculate the ratio. Once you find the correct numerical value, you can choose the corresponding answer from the given options.
electro:
Fe= k Q1 Q2 /d^2 = 9 * 10^9 *(1.6*10^-19 )^2 / d^2
gravity:
Fg = G M1 M2 /d^2= 6.7*10^-11* (9.1*10^-31)^2 / d^2
ratio:
Fg/Fe = 6.7*10^-11* (9.1*10^-31)^2 / 9 * 10^9 *(1.6*10^-19 )^2
(gravity loses huge for small objects with serious charge)