A sprinter must average 24.0 mi/h to win a 100-m dash in 9.30 s. What is his wavelength at this speed if his mass is 84.5 kg?

Answer: 7.31*10^-37

Explanation:

Given

Speed of sprinter, v = 24 mi/h

Distance to run, d = 100 m

Time needed for the run, t = 9.3 s

Mass of sprinter, m = 84.5 kg

Wavelength of sprinter, λ = ?

To solve this question, we would be using De Broglie's wavelength.

λ = h/mv, where

λ = wavelength

h = Planck's constant = 6.63*10^-34 m²kg/s

m = mass

v = velocity

To start with, we convert the speed of the sprinter from mi/h to m/s

v = 24 mi/h

1 mile = 1609 m

1 hour = 3600 s

24 mi/h = (24 * 1609) / 3600

24 mi/h = 38616 / 3600

24 mi/h = 10.73 m/s

λ = 6.63*10^-34 / 84.5 * 10.73

λ = 6.63*10^-34 / 906.685

λ = 7.31*10^-37

Therefore, the wavelength of the sprinter is 7.31*10^-37 m

Wavelength λ = 7.31 * 10^-37 m

Explanation:

From De Broglie's equation;

λ = h/mv

Where;

λ = wavelength in meters

h = plank's constant = 6.626*10^-34 m^2 kg/s

m = mass in kg

v = velocity in m/s

Given;

v = 24 mi/h

Converting to m/s

v = 24mi/h * 0.447 m/s * 1 / (mi/h)

v = 10.73m/s

m = 84.5kg

Substituting the values into the equation;

λ = (6.626*10^-34 m^2 kg/s) / (84.5kg * 10.73m/s)

λ = 7.31 * 10^-37 m