An Oxygen Molecule $\mathrm { O } _ { 2 } ,$

Multiple Choice

An oxygen molecule, $\mathrm { O } _ { 2 } ,$ falls in a vacuum. From what height must it fall so that its translational kinetic energy at the bottom of its fall equals the average translational kinetic energy of an oxygen molecule at 920 K? The mass of one $\mathrm { O } _ { 2 }$ molecule is $5.312 \times 10 ^ { - 26 } \mathrm {~kg}$ and the Boltzmann constant is $1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K }$ Neglect air resistance and assume that g remains constant at $9.8 \mathrm {~m} / \mathrm { s } ^ { 2 }$ throughout the fall of the molecule.

A) 5.2 km
B) 12 km
C) 49 km
D) 37 km
E) 24 km