Question

in 1990, the men's singles winner of the us. open tennis tournament has his serves clocked at 127 mi/hr. How fast must a 56.6 g tennis ball travel to have a de Broglie wavelength equal to that of a photon of green light (5400 A)?

Answer 1

This problem is providing information about the mass of a tennis ball, 56.6 g (0.0566 kg) and asks for the velocity it will have to equal the wavelength of green light, which is 5400 A or 540 nm (5.4x10⁻⁷ m). Thus, after doing the math, the result is 2.17x10⁻²⁶ m/s.

Broglie's wavelength:

In this case, we recall the formula of the Broglie's wavelength as shown below:

$\lambda =\frac{h}{mv}$

Whereas lambda is the wavelength, h is the Planck's constant, m the mass and v the speed; thus, we solve for the speed according to the question:

$v =\frac{h}{m\lambda}$

Calculations:

Then, we just plug in the numbers we were given to get the answer:

$v =\frac{6.626x10^{-34} kg*\frac{m^2}{s} }{0.056kg*5.4x10^{-7}m}\\\\v=2.17x10^{-26}m/s$

Learn more about Broglie's wavelength: brainly.com/question/5440536