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

Multiple Choice

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

A) $\frac { d L } { d t } = \frac { 2 } { \sqrt { 2 } \pi t ^ { 3 } n }$
B) $\frac { \mathrm { dL } } { \mathrm { dt } } = \frac { 1 } { 2 \sqrt { 2 } \pi \mathrm { t } ^ { 3 } \mathrm { n } }$
C) $\frac { \mathrm { dL } } { \mathrm { dt } } = - \frac { 2 } { \sqrt { 2 } \pi \mathrm { t } ^ { 3 } \mathrm { n } }$
D) $\frac { \mathrm { dL } } { \mathrm { dt } } = - \frac { 1 } { \sqrt { 2 } \pi \mathrm { tn } }$