What is the speed of an average argon atom that has a de Broglie wavelength of 5.2 pm? (1 amu = 1.66054 $\times$ 10^-27 kg)

Question

Quizplus · Accepted Answer

The de Broglie wavelength of a particle can be calculated using the equation: λ = h/mv, where h is Planck's constant, m is the mass of the particle, v is its velocity, and λ is the wavelength.
Rearranging the equation to solve for v gives: v = h/(mλ).
Plugging in the values given in the problem: 
λ = 5.2 pm = 5.2 × 10^-12 m
m = 40 amu = 40 × 1.66054 × 10^-27 kg/amu = 6.64216 × 10^-26 kg
h = 6.62607 × 10^-34 J·s
v = (6.62607 × 10^-34 J·s)/(6.64216 × 10^-26 kg × 5.2 × 10^-12 m) = 1.9 × 10^3 m/s = 1.9 km/s.
Therefore, the correct choice is C, 1.9 × 10^3 m/s.

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