When two identical ions are separated by a distance of 4.0×10^−10 , the electrostatic force each exerts on the other is 5.7×10^−9 .
How many electrons are missing from each ion?
what i did was used coulombs law to find the value of q1 and q2 , so q1+q2=1.013333333^-37
Now would i divide that by 4 since the number of + and - charges are suppose to add up to that number and also there are 2 ions??
To determine the number of missing electrons from each ion, let's break down the process step by step.
1. Begin by recalling Coulomb's law, which states that the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
In this case, we have two identical ions, so we can assume that they carry the same charge, q, and the force between them is given as 5.7×10^−9 N.
Therefore, Coulomb's law can be expressed as F = k(q_1)(q_2) / r^2, where F is the force, k is the Coulomb's constant, q_1 and q_2 are the charges on the ions, and r is the distance between them.
2. Rearranging the equation, we get (q_1)(q_2) = Fr^2 / k.
3. Now, substitute the given values into the equation:
F = 5.7×10^−9 N
r = 4.0×10^−10 m
k = 9.0×10^9 N·m^2/C^2
Plugging in these values, we obtain (q_1)(q_2) = (5.7×10^−9 N)(4.0×10^−10 m)^2 / (9.0×10^9 N·m^2/C^2).
Simplifying the expression, we find (q_1)(q_2) = 1.6×10^−28 C^2.
4. Since the ions are identical, the charges, q_1 and q_2, will be the same. Therefore, we can write (q_1)(q_2) = q^2.
So, q^2 = 1.6×10^−28 C^2.
5. To find the value of q, take the square root of both sides: q = √(1.6×10^−28 C^2).
Using a calculator, the calculated value is approximately q = 1.3×10^−14 C.
6. Each electron carries a charge of -1.6×10^−19 C. Therefore, to find the number of missing electrons from each ion, divide the total charge (q) by the charge per electron:
Number of missing electrons = q / (-1.6×10^−19 C) = (1.3×10^−14 C) / (-1.6×10^−19 C).
By dividing these values, you'll obtain the number of missing electrons from each ion.
Remember to account for the negative sign since the ions are missing electrons, which have a negative charge.