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 ? (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.

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Quizplus · Accepted Answer

The de Broglie wavelength is given by:$$\lambda = \frac{h}{p} = \frac{h}{mv}$$where:* $$\lambda$$ is the wavelength* $$h$$ is the Planck constant* $$p$$ is the momentum* $$m$$ is the mass* $$v$$ is the velocityWe are given:* $$m = 84.5 	ext{ kg}$$* $$v = 24.0 	ext{ mi/h} = 10.7 	ext{ m/s}$$* $$h = 6.63 	imes 10^{-34} 	ext{ J} \cdot 	ext{s}$$First, we need to convert the velocity to m/s:$$v = 24.0 	ext{ mi/h} = 10.7 	ext{ m/s}$$Now, we can plug in the values:$$\lambda = \frac{h}{mv} = \frac{6.63 	imes 10^{-34} 	ext{ J} \cdot 	ext{s}}{(84.5 	ext{ kg})(10.7 	ext{ m/s})} = 7.31 	imes 10^{-37} 	ext{ m}$$Therefore, the correct answer is A.

A Sprinter Must Average 24