Final answer:
In the Bohr model of the atom, the radius of the orbit can be calculated using the speed and time taken for one orbit. By rearranging the formula for speed, we can determine the distance traveled by the electron in one orbit. Using the circumference formula for a circle, the radius of the orbit can be calculated by dividing the distance by 2π.
Step-by-step explanation:
In the Bohr model of the atom, the electron travels in a circular orbit around the nucleus. The speed of the electron is given as 2.2 x 10^6 m/s and the time taken for one orbit is 1.5 x 10^-16 s. We can use the formula for the circumference of a circle to calculate the radius of the orbit.
The circumference of the orbit is equal to the distance traveled by the electron in one orbit. Using the formula for speed, which is speed = distance/time, we can rearrange the formula to solve for distance: distance = speed x time. Plugging in the given values, we have: distance = 2.2 x 10^6 m/s x 1.5 x 10^-16 s. Simplifying this gives us the distance traveled in one orbit.
The circumference of the orbit is equal to 2π times the radius of the orbit. Therefore, we can set up the equation: 2πr = distance traveled. Solving for r, we find that the radius of the orbit is equal to the distance traveled divided by 2π. Plugging in the distance traveled value, we can calculate the radius of the orbit.