A) \[\frac{\text{1}}{\text{2}}\sqrt{\text{15}}\text{km}{{\text{s}}^{\text{-1}}}\]
B) \[\frac{\text{1}}{\text{2}}\sqrt{\text{10}}\text{km}{{\text{s}}^{\text{-1}}}\]
C) \[\text{2}\text{.5km}{{\text{s}}^{\text{-1}}}\]
D) \[\sqrt{\frac{15}{2}}\text{km}{{\text{s}}^{\text{-1}}}\]
Correct Answer: D
Solution :
The square root of \[{{\bar{v}}^{2}}\]is called the root mean square velocity (rms) speed of the molecules. \[{{v}_{rms}}=\sqrt{{{{\bar{v}}}^{2}}}\] \[=\sqrt{\frac{{{v}_{1}}^{2}+{{v}_{2}}^{2}+{{v}_{3}}^{2}+{{v}_{4}}^{2}}{4}}\] \[=\sqrt{\frac{{{(1)}^{2}}+{{(2)}^{2}}+{{(3)}^{2}}+{{(4)}^{2}}}{4}}\] \[=\sqrt{\frac{1+4+9+16}{4}}\] \[=\sqrt{\frac{30}{4}}\] \[=\sqrt{\frac{15}{2}}km{{s}^{-1}}\]
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