Question

15. The planetary model of the atom pictures electrons orbiting the atomic nucleus much as planets orbit the Sun. In this model you can view hydrogen, the simplest atom, as having a single electron in a circular orbit 1.06×10−10m in diameter. (a) If the average speed of the electron in this orbit is known to be 2.20×106m/s, calculate the number of revolutions per second it makes about the nucleus. (b) What is the electron’s average velocity?

Answer 1

In this model, the electron makes 6.59 × 10^15 revolutions per second and has an average velocity of 2.20 × 10^6 m/s per revolution.

Step-by-step explanation:

(a) To calculate the number of revolutions per second, we need to find the time taken for one revolution around the nucleus. The circumference of the circular orbit can be calculated using the formula C = 2πr, where r is the radius of the orbit. Since the diameter is given as 1.06 × 10-10 m, the radius is half of that value. Plugging in the values, C = 2π(1.06×10-10/2) = 3.34 × 10-10 m. Now, we can calculate the time taken for one revolution using the formula T = Δs/v, where T is the time, Δs is the circumference, and v is the velocity. Plugging in the values, T = (3.34 × 10-10) / (2.20 × 106) = 1.52 × 10-16 s. Therefore, the electron makes 1 / T = 6.59 × 1015 revolutions per second.

(b) The average velocity of the electron can be calculated using the formula v = Δs / Δt, where v is the velocity, Δs is the circumference, and Δt is the time. Plugging in the values, v = (3.34 × 10-10) / (1.52 × 10-16) = 2.20 × 106 m/s. Therefore, the electron's average velocity per revolution is 2.20 × 106 m/s.

Answer 2

a) 6.6 * 10^15 (1/s)

b) 0 m/s

Step-by-step explanation:

Hi!

a)

In order to complete a revolution the electron must travel a distance d, where d is the perimeter of the circular orbit:

d = π(1.06*10^-10 m) = 3.33 * 10^-10 m

Therefore, the number of revolutions per second the electron makes about the nucleus is:

n = (2.20×10^6m/s) / d = 0.66 * 10^16 (1/s)

b)

Since the electron is travelling in a circular orbit, the average velocity must be zero. That is because the velocity is a vector and the direction of the velocity at one point on the circle is opposite at an opposite point of the same circle. When adding these two (arbitrary points) they will cancel each other