at what distance would repulisve force between two electrons have a magnitude of 2.00 n between two protons ?
2=kq1q2/r^2
r^2 = 9.0 x10^9 x (1.6 x 10^-19)^2
So, what is the R, on my answer from, this is 1.07 x10^-14m,
however, I cannot get this, can you show me how to get it ?
See Related questiond, below, #2, look at the answer, follow the link
hello! in order to get the correct answer, you need to divide the entire problem by two and then take the square root
Well, my dear friend, let's calculate this together with a sprinkle of humor!
We have the equation 2 = kq1q2/r^2, where k is the Coulomb's constant, q1 and q2 are the charges, and r is the distance between them.
First, let's evaluate the Coulomb's constant. It's like Excel's constant, but for electric charges! It's approximately 9.0 x 10^9. Easy-peasy!
Next up, let's compute the product of the charges squared: (1.6 x 10^-19)^2. This gives us an answer of approximately 2.56 x 10^-38.
Now comes the fun part! Divide this product by 2 to find the actual repulsive force: 2.56 x 10^-38 / 2 = 1.28 x 10^-38.
Finally, to find the distance r, we rearrange the equation to solve for it: r^2 = kq1q2/F. Plugging in the values, we have r^2 = (9.0 x 10^9)(1.6 x 10^-19)^2 / 1.28 x 10^-38.
Now, when we crank the numbers, we get a rootin' tootin' answer of r ≈ 1.07 x 10^-14 meters! Ta-da!
So now you have the distance between those feisty electrons and protons with a repulsive force magnitude of 2.00 n. But don't let them get too close, or there'll be some static tension at the atomic party!
To find the distance (r) at which the repulsive force between two protons is 2.00 N, we can use Coulomb's Law:
F = (k * q1 * q2) / r^2
where:
F is the magnitude of the force (2.00 N)
k is the electrostatic constant (9.0 x 10^9 N·m^2/C^2)
q1 and q2 are the charges of the two protons (both +1.6 x 10^-19 C)
Rearranging the formula, we get:
r^2 = (k * q1 * q2) / F
Substituting the given values:
r^2 = (9.0 x 10^9 N·m^2/C^2) * ((1.6 x 10^-19 C)^2) / (2.00 N)
r^2 = 1.152 x 10^-28 (m^3/C^2) / N
To simplify this, we can convert the units:
(N·m^2/C^2) = (kg·m/s^2)·m^2 / (C^2) = kg·m^3/(C^2·s^2)
So, substituting the unit conversion:
r^2 = 1.152 x 10^-28 (kg·m^3)/(C^2·s^2) / N
To cancel out the second in the denominator, we can multiply by the reciprocal:
r^2 = 1.152 x 10^-28 (kg·m^3)/(C^2·s^2) * (1 s^2 / N)
r^2 = 1.152 x 10^-28 (kg·m^3)/(C^2·N)
Now, we can calculate:
r^2 = 1.152 x 10^-28 (1.6 x 10^-19)^2 C^2 / (2.00)
Calculating this value gives us:
r^2 ≈ 9.216 x 10^-47 m^2
To find r, we take the square root of both sides:
r ≈ √(9.216 x 10^-47) m
Calculating this, we get:
r ≈ 3.04 x 10^-24 m
So, the distance at which the repulsive force between two protons has a magnitude of 2.00 N is approximately 3.04 x 10^-24 meters.
To find the distance at which the repulsive force between two electrons or two protons has a magnitude of 2.00 N, you can use Coulomb's Law equation:
F = k * |q1 * q2| / r^2
Where:
F is the magnitude of the electrostatic force
k is Coulomb's constant, approximately 9.0 x 10^9 N·m^2/C^2
|q1 * q2| is the product of the magnitudes of the charges of the two particles
r is the distance between the charges
In this case, the magnitudes of the charges for both electrons and protons are the same and equal to 1.6 x 10^-19 C.
Rearranging the equation, we get:
r^2 = k * |q1 * q2| / F
Substituting the known values, we have:
r^2 = (9.0 x 10^9 N·m^2/C^2) * (1.6 x 10^-19 C)^2 / (2.00 N)
Simplifying, we get:
r^2 = (9.0 x 10^9 N·m^2/C^2) * (2.56 x 10^-38 C^2) / (2.00 N)
The units of N·m^2/C^2 and C^2 cancel out, leaving us with:
r^2 = 12.96 x 10^-29 m^2 / N
To find r, we take the square root of both sides:
r = √(12.96 x 10^-29 m^2 / N)
Evaluating this expression, we find:
r ≈ 1.07 x 10^-14 m
So, the distance at which the repulsive force between two electrons or two protons has a magnitude of 2.00 N is approximately 1.07 x 10^-14 meters.