Answer

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**Hint:**

According to the kinetic theory of matter, the molecules of a gas are always in a state of ceaseless motion with a frequent collision with each other. As the molecules collide there is a transfer of energy from one molecule to the other. Due to this transfer of energy, the molecules which gain energy their velocity increases, while which loses energy their velocity decreases.

**Complete answer:**

Step 1

As we study the different properties of gases, there are three types of molecular velocities about which we need to know.

They are:

Average velocity – At a particular temperature average velocity is the arithmetic mean of the different velocities of different molecules of the gas. From Maxwell’s equation, the mathematical expression for average velocity is given by \[\mathop u\limits^ - = \sqrt {\frac{{8RT}}{{\pi M}}} \]where M is the molecular mass of the gas, R is the Universal gas constant and T is the absolute temperature.

Root mean-square velocity – At a particular temperature the square root of the arithmetic mean of the squares of velocities for different molecules of a gas is known as the root mean square velocity or RMS velocity of the gas. The value of RMS velocity is calculated with the help of a kinetic gas equation and is given by \[u = \sqrt {\frac{{3RT}}{M}} \].

Most probable velocity – at a particular temperature the velocity possessed by the majority fraction of the molecules is known as the most probable velocity. The mathematical expression for the most probable velocity is given by \[\alpha = \sqrt {\frac{{2RT}}{M}} \].

Step 2

In the given question the rms velocity of hydrogen gas is \[2400m/s\] and the molecular mass for hydrogen is \[2\].

We know, \[u = \sqrt {\frac{{3RT}}{M}} \]

\[\therefore \sqrt {\frac{{3RT}}{2}} = 2400\]

Taking square on both sides, we have

\[\therefore \frac{{3RT}}{2} = 2400 \times 2400\]

\[\therefore RT = 2400 \times 2400 \times \frac{2}{3}\]

Step 3

For oxygen molecules the molecular mass is \[32\].

\[u = \sqrt {\frac{{3RT}}{M}} \]

Putting the value of RT we get,

\[\therefore u = \sqrt {\frac{{3 \times 2400 \times 2400 \times 2}}{{32 \times 3}}} \]

\[\therefore u = 6 \times 100\]

\[\therefore u = 600m/s\]

**Hence, we can find that it is option c) which is the correct answer for the given question.**

**Note:**With the increase in temperature, more molecules have higher velocities and fewer will have lower velocities and vice-versa. At absolute zero, the molecules of gas become perfectly motionless and become nonexistent. Thus the absolute scale of temperature is always positive.

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