A sprinter must average 24.0 mi/h to win a 100-m dash in 9.30 s. What is his de Broglie wavelength at this speed if his mass is 84.5 kg ? (h = 6.63 × 10^-34 J • s) A) 7.31 × 10^-37 m B) 3.26 × 10^-37 m C) 5.08 × 10^-30 m D) 1.34 × 10^-30 m E) None of these choices is correct.

Question

Quizplus · Accepted Answer

The de Broglie wavelength is given by the equation λ = h/p, where h is Planck's constant and p is the momentum of the object. The momentum of the sprinter is given by p = mv, where m is his mass and v is his velocity. Substituting these equations into the first equation, we get λ = h/mv. Plugging in the given values, we get λ = (6.63 × 10^-34 J • s)/(84.5 kg * 24.0 mi/h * 1609.34 m/mi * 1 h/3600 s) = 7.31 × 10^-37 m.

A Sprinter Must Average 24