In the Bohr theory of the hydrogen atom, an electron moves in a circular orbit about a proton, where the radius of the orbit is approximately 0.542 multiplied by 10-10 m. (The actual value is 0.529 multiplied by 10-10 m.)
(a) Find the electric force exerted on each particle, based on the approximate (not actual) radius given
To find the electric force exerted on each particle, we can use Coulomb's law, which states that the force between two charged particles is given by:
F = (k * |q1 * q2|) / r^2
Where F is the electric force, k is the electrostatic constant (approximately 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 the case of the hydrogen atom, the electron carries a negative charge (-e) and the proton carries a positive charge (+e), where e is the elementary charge (approximately 1.6 x 10^-19 C).
Given that the radius of the electron's orbit is approximately 0.542 x 10^-10 m (0.542 Å or 0.542 Angstroms), we can substitute the values into the formula and calculate the force:
F = (k * |-e * +e|) / (0.542 x 10^-10 m)^2
Now, let's calculate the electric force exerted on each particle using the approximate radius given:
F = (9.0 x 10^9 N*m^2/C^2 * |-1.6 x 10^-19 C * 1.6 x 10^-19 C|) / (0.542 x 10^-10 m)^2
F = (9.0 x 10^9 N*m^2/C^2 * 2.56 x 10^-38 C^2) / (0.542 x 10^-10 m)^2
F = 1.44 x 10^-28 N
Therefore, the approximate electric force exerted on each particle in the Bohr model of the hydrogen atom is approximately 1.44 x 10^-28 N.