# Imat 2018 question 59

Hello, why is statement 4 not correct?

The Earth’s atmosphere contains oxygen and nitrogen. The mass of an oxygen molecule is greater than the mass of a nitrogen molecule. The temperature of air in a room on a particular day is 300 K.

Below are four statements about the motion of the two types of molecule in this room.

They have an equal mean square velocity \overline{(v^2)}.

A nitrogen molecule has a greater mean square velocity \overline{(v^2)} than an oxygen molecule.

A nitrogen molecule has a greater mean kinetic energy than an oxygen molecule.

An oxygen molecule has a greater mean kinetic energy than a nitrogen molecule.

Which of the statements is/are correct?

A. statement 1 only
B. statement 1 and 3 only
C. none of them
D. statement 2 only
E. statement 2 and 4 only

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The kinetic energy of both molecules stay the same as the temperature remains the same. You can use 1/2 mv^2 as reference

oxygen has a greater mass but lower velocity
nitrogen has a low mass but greater velocity (it’s light so it travels faster) so when mass increases and velocity decreases proportionally the kinetic energy remains the same.

Hope this explanation helps! It’s what I used to understand it simply

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