"Suppose some sort of clamp is applied to hold an electron fixed at the distance of 2.5 Angstroms from a lithium nucleus Li3+ which is also clamped into position. Calculate the magnitude of the force between the two fixed particles."
The books says the answer is:
-2.304 x 10^-9 N
I've tried the problem several times and keep getting:
-1.107x10^-8 N
I've been using the equation
F(r) = [(q1)(q2)/[(4)(PI)(Epsilon naught)(r^2)]
Could someone please help me out? Thank you.
To calculate the magnitude of the force between two charged particles, we can indeed use Coulomb's law, which is given by the equation:
F = (k * |q1 * q2|) / r^2
Here, F represents the magnitude of the force between the two particles, q1 and q2 are the charges of the particles, r is the distance between them, and k is Coulomb's constant.
In this problem, we are given that an electron (charge q1 = -1.6 x 10^-19 C) is held fixed at a distance of 2.5 Å (2.5 x 10^-10 m) from a lithium nucleus (charge q2 = +3e, where e is the elementary charge e = 1.6 x 10^-19 C). We need to find the magnitude of the force between them.
Substituting the given values into the equation, we get:
F = (k * |-1.6 x 10^-19 * 3e|) / (2.5 x 10^-10)^2
Now, we need to evaluate Coulomb's constant, k. Coulomb's constant is defined as:
k = (1 / (4πε0))
Where ε0 is the permittivity of free space, and its value is approximately ε0 = 8.854 x 10^-12 C^2 / (N ∙ m^2).
Plugging in the values of k and the charges into the equation, we have:
F = ((1 / (4πε0)) * |-1.6 x 10^-19 * 3e|) / (2.5 x 10^-10)^2
Simplifying further, we find:
F = ((1 / (4πε0)) * 4.8 x 10^-19) / (2.5 x 10^-10)^2
Now, substitute the value of ε0 and evaluate the expression:
F = ((1 / (4π(8.854 x 10^-12 C^2 / (N ∙ m^2)))) * 4.8 x 10^-19) / (2.5 x 10^-10)^2
F = ((1 / (4π(8.854 x 10^-12))) * 4.8 x 10^-19) / (6.25 x 10^-20)
F = (9 x 10^9 * 4.8 x 10^-19) / (6.25 x 10^-20)
Now, calculate the division:
F = (43.2 x 10^-10) / (6.25 x 10^-20)
F ≈ -6.912 N
However, there seems to be a discrepancy between the answer you obtained (-1.107 x 10^-8 N) and the answer provided in the book (-2.304 x 10^-9 N). It's possible that there may be a mistake in the calculation or a difference in the values used. I would recommend revisiting the calculations and double-checking for any errors.