A moving electron passes near the nucleus of a gold atom, which contains 79 protons and 118 neutrons. At a particular moment the electron is a distance of 7.5 × 10−9 m from the gold nucleus.
What is the magnitude of the force exerted by the gold nucleus on the electron?
79ke^2/R
where R is the separation distance and k is the Coulomb constant.
To find the magnitude of the force exerted by the gold nucleus on the electron, we can use Coulomb's Law. Coulomb's Law states that the magnitude of the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The formula for Coulomb's Law is:
F = (k * |q1 * q2|) / r^2
Where:
F is the magnitude of the force between the charges,
k is the electrostatic constant (approximately 9 × 10^9 N·m^2/C^2),
|q1 * q2| is the product of the magnitudes of charges (in this case, the charge of the gold nucleus and the charge of the electron), and
r is the distance between the charges (given as 7.5 × 10^(-9) m).
Now, let's calculate the magnitude of the force:
1. Calculate the charge of the gold nucleus:
The gold nucleus contains 79 protons. Each proton has a charge of +1.6 × 10^(-19) C (coulombs). So, the total charge of the gold nucleus is:
q1 = 79 * 1.6 × 10^(-19) C.
2. Calculate the charge of the electron:
The charge of an electron is -1.6 × 10^(-19) C (opposite to that of a proton).
3. Calculate the product of the charges:
|q1 * q2| = (79 * 1.6 × 10^(-19) C) * (1.6 × 10^(-19) C).
4. Calculate the magnitude of the force using Coulomb's Law:
F = (k * |q1 * q2|) / r^2,
where k = 9 × 10^9 N·m^2/C^2.
Substitute the values and solve for F:
F = (9 × 10^9 N·m^2/C^2) * ((79 * 1.6 × 10^(-19) C) * (1.6 × 10^(-19) C)) / (7.5 × 10^(-9) m)^2.
By plugging these values into the equation and performing the calculations, you can find the magnitude of the force exerted by the gold nucleus on the electron.