Dust Particles in a Grain Elevator Frequently Have Masses of the Order

Dust particles in a grain elevator frequently have masses of the order of $1.0 \times 10 ^ { - 9 } \mathrm {~kg}$
If, to a first approximation, we model the dust particles as an ideal gas, what would be the rms speed of such a particle in air at $27 ^ { \circ } \mathrm { C } \text { ? }$ The Boltzmann constant is $1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K }$

A) $5.6 \times 10 ^ { - 5 } \mathrm {~m} / \mathrm { s }$
B) $7.8 \times 10 ^ { - 4 } \mathrm {~m} / \mathrm { s }$
C) $3.5 \times 10 ^ { - 6 } \mathrm {~m} / \mathrm { s }$
D) $5.2 \times 10 ^ { - 3 } \mathrm {~m} / \mathrm { s }$
E) $4.9 \times 10 ^ { - 2 } \mathrm {~m} / \mathrm { s }$

Correct Answer:

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