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Physics Question on kinetic theory

The respective speeds of five molecules are 2, 1.5, 1.6, 1.6 and 1.2 km s−11.2 \, km \, s^{-1}, the most probable speed in km s−1{km\, s^{-1}} will be

A

2

B

1.58

C

1.6

D

1.31

Answer

1.31

Explanation

Solution

vmp=0.816 vrmsv_{mp} = 0.816 \, v_{rms}
=0.816v12+v22+v32+v42+v52N= 0.816 \sqrt{\frac{v^{2}_{1}+v_{2}^{2}+v_{3}^{2}+v_{4}^{2}+v_{5}^{2}}{N}}
=0.816(2)2+(1.5)2+(1.6)2+(1.6)2+(1.2)25=0.816 \sqrt{\frac{\left(2\right)^{2}+\left(1.5\right)^{2} +\left(1.6\right)^{2} +\left(1.6\right)^{2}+\left(1.2\right)^{2}}{5}}
=1.31 Km s−1= 1.31 \, Km \, s^{-1}