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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?
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Helga
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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
Answer:
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