Question

An electron is orbiting a proton 8.0 cm away. at what velocity is the electron traveling?

Answer 1

The velocity of the electron traveling in a circular orbit around the proton is approximately 2.188 x 10^6 m/s.

Step-by-step explanation:

In the simple Bohr model of the hydrogen atom, the electron travels in a circular orbit around a fixed proton. The formula to calculate the velocity of an electron in a circular orbit is v = (ke^2/mr)^(1/2), where ke is the electrostatic constant, e is the charge of an electron, m is the mass of an electron, and r is the radius of the orbit.

To find the velocity, we need to know the values of ke, e, and m. In this case, we're given the radius of the orbit as 8.0 cm, which can be converted to meters as 0.08 m. The charge of an electron is -1.6 x 10^(-19) C and the mass of an electron is 9.1 x 10^(-31) kg. The electrostatic constant ke is approximately 8.99 x 10^9 Nm^2/C^2.

Substituting the values into the formula, we get:

v = (8.99 x 10^9 x (-1.6 x 10^(-19))^2 / (9.11 x 10^(-31) x 0.08))^1/2

Simplifying the equation, we get:

v = 2.188 x 10^6 m/s

Therefore, the velocity of the electron traveling in a circular orbit around the proton is approximately 2.188 x 10^6 m/s.

Answer 2

To find the velocity of an electron in a circular orbit around a proton, you can use the formula velocity = (momentum) / (mass of the electron).

Step-by-step explanation:

In the simple Bohr model of the ground state of the hydrogen atom, the electron moves in a circular orbit around the proton. The velocity of the electron can be calculated using the formula:

velocity = (momentum) / (mass of the electron)

Using the given momentum of 3.04×10-21 kg·m/s and the mass of the electron, which is 9.11×10-31 kg, we can substitute these values into the formula to find the velocity.