Provide an Appropriate Response $\mathrm { L } = \frac { 1 } { \sqrt { 2 } \pi \mathrm { t } ^ { 2 } \mathrm { n } }$

Multiple Choice

Provide an appropriate response.
-Under standard conditions, molecules of a gas collide billions of times per second. If each molecule has diameteı average distance between collisions is given by
$\mathrm { L } = \frac { 1 } { \sqrt { 2 } \pi \mathrm { t } ^ { 2 } \mathrm { n } }$ where $n$ , the volume density of the gas, is a constant. Find $\frac { d ^ { 2 } L } { d t ^ { 2 } }$ .

A) $\frac { \mathrm { d } ^ { 2 } \mathrm {~L} } { d t ^ { 2 } } = - \frac { 2 } { \sqrt { 2 } \pi t ^ { 3 } n }$
B) $\frac { d ^ { 2 } L } { d t ^ { 2 } } = \frac { 6 } { \sqrt { 2 } \pi t ^ { 4 } n }$
C) $\frac { \mathrm { d } ^ { 2 } \mathrm {~L} } { \mathrm { dt } ^ { 2 } } = - \frac { 2 } { \sqrt { 2 } \pi \mathrm { t } ^ { 2 } \mathrm { n } }$
D) $\frac { \mathrm { d } ^ { 2 } \mathrm {~L} } { \mathrm { dt } ^ { 2 } } = - \frac { 6 } { \sqrt { 2 } \pi t ^ { 4 } \mathrm { n } }$