Question

A bowling ball weighs 12.0 pounds and the length of a bowling lane is 60 feet, assume that you can treat the ball in the lane as a particle on a line. What is the quantum number that corresponds to the balls velocity of 7.55 miles per hour?

Answer 1

Answer on Question #65608, Physics / Mechanics | Relativity

A bowling ball weighs 12.0 pounds and the length of a bowling lane is 60 feet, assume that you can treat the ball in the lane as a particle on a line. What is the quantum number that corresponds to the balls velocity of 7.55 miles per hour?

Solution:

$$E = \frac{1}{2} m v^2$$ $$m = 12.0 \text{ pounds} = 5.4 \text{ kg}$$ $$v = 7.55 \text{ miles/hour} = 3.38 \text{ ms}^{-1}$$ $$a = 60 \text{ feet} = 18.3 \text{ m}$$ $$E = \frac{1}{2} \times 5.4 \text{ kg} \times (3.38 \text{ ms}^{-1})^2 = 30.8 \text{ J}$$ $$E = \frac{n^2 h^2}{8 m a^2}$$ $$n^2 = 8 E m a^2 / h^2$$ $$n^2 = 8 \times 30.8 \text{ J} \times 5.4 \text{ kg} \times (18.3 \text{ m})^2 / (6.62 \times 10^{-34})^2 = 1.02 \times 10^{72}$$ $$n = 10^{36}$$

Answer: $10^{36}$

Answer provided by https://www.AssignmentExpert.com