A hydroxide ion (OH−) in a glass of water has an average speed of about 600 m/s.
Determine the magnitude of the electrical force between the hydroxide ion (charge -e) and a positive ion (charge +e) that is 1.0×10−8 m away (about the separation of 30 atoms).
To determine the magnitude of the electrical force between the hydroxide ion (OH-) and a positive ion (+e), we can use Coulomb's law. Coulomb's law states that the electrical force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of their distance.
The mathematical formula for Coulomb's law is:
F = k * (q1 * q2) / r^2
where:
F is the electrical force between the particles,
k is the electrostatic constant, approximately equal to 9.0 x 10^9 N m^2 / C^2,
q1 and q2 are the charges of the particles, and
r is the distance between them.
In our case, the charge of the hydroxide ion (OH-) is -e (negative charge), and the charge of the positive ion is +e (positive charge). The distance between them, r, is 1.0 x 10^-8 m.
We substitute these values into Coulomb's law:
F = (9.0 x 10^9 N m^2 / C^2) * ((-e) * (+e)) / (1.0 x 10^-8 m)^2
Now, we need to find the value of the charge -e. The charge of an electron, which is the same as the hydroxide ion, is approximately -1.6 x 10^-19 C.
Substituting this value into the equation:
F = (9.0 x 10^9 N m^2 / C^2) * ((-1.6 x 10^-19 C) * (+1.6 x 10^-19 C)) / (1.0 x 10^-8 m)^2
Now, we can simplify and calculate the result:
F = (9.0 x 10^9 N m^2 / C^2) * (-2.56 x 10^-38 C^2) / (1.0 x 10^-16 m^2)
= -2.3 x 10^-13 N
The magnitude of the electrical force between the hydroxide ion and the positive ion is approximately 2.3 x 10^-13 N.
What is k q1q2/distance^2. q1=1.6*10^-19, q2=same (ignore signs). distance^2=1e-16
force=2.3e-28/1e-16=2.3e-12N