Question

The respectively speeds of five molecules are \[2,1.5,1.6,1.6\] and \[1.2km/sec\] the most probable speed in km/sec will be:
A. \[2\]
B. \[1.58\]
C. \[1.6\]
D. \[1.31\]

Answer 1

Hint: The ability of the movements of an object to do work is known as the energy. The measurement of the volume of the object is known as the momentum.
The inertial momentum based on the mass of the object.

Complete step by step answer:
The energy can be converted into other kinds of energy like that electric potential energy or gravitational energy.
The product of the half of the mass of each gas molecule and the square of RMS speed is known as the average kinetic energy.
If it doesn’t do some work or gain some potential the kinetic energy will be reversed automatically. The momentum is directly proportional to the mass and velocity of the object and it is also a vector quantity. and the kinetic energy is a scalar quantity and it is directly proportional to the magnitude of the object velocity and the object mass.
The gas molecule’s RMS velocity is calculated by the as follows,
\[{V_{rms}} = \sqrt {\left[ {\dfrac{{\left( {{2^2} + {{1.5}^2} + {{1.6}^2} + {{1.6}^2} + {{1.2}^2}} \right)}}{5}} \right]} \]
Now solve the above we get the value of \[{V_{rms}}\]
\[{V_{rms}} = \sqrt {\dfrac{{12.8}}{5}} \]
After simplification,
\[{V_{rms}} = 1.6m/s\]
Then the most probable speed is calculated as follows,
\[{V_{mp}} = \sqrt {\dfrac{2}{3} \times } {V_{rms}}\]
Now substitute the value of the \[{V_{rms}}\]in the above equation we get,
\[{V_{mp}} = 0.816 \times 1.6\]
And finally the most probable speed is ,
\[{V_{mp}} = 1.306km/s\]
Hence, the correct answer is option (D).

Note: The kinetic energy is related with the movement.
If we increase the velocity then the kinetic energy also gets increased.
Some examples of the kinetic energy are A flying bird, and the planets rotates around the sun.