A 9-kg body has three times the kinetic energy of an 4-kg body. Calculate the ratio of the speeds of these bodies.
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The rms speed of the molecules of gas A is twice that of gas B. The molecular mass of A is one fourth to that of B.
Answer: Option B
<u>Explanation:</u>
Measuring the speed of particles at a given point in time results in a large distribution of values. Some molecules can move very slowly, others very fast, and because they are still moving in different directions, the speeds may be zero. (Velocity, vector quantity that corresponds to the speed and direction of the molecule.)
To correctly estimate the average velocity, you must take the squares of the mean velocity and take the square root of this value. This is known as the root mean square (rms) velocity and is shown as follows:
Where,
M – Gas’s molar mass
R – Molar mass constant
T – Temperature (in Kelvin)
Given data is rms speed for gas molecule A is twice that of gas molecule B. So,
Therefore, equating the molecule’s rms speed formula for both A and B,
On squaring both sides, we get,
By solving the above equations, we get,
To solve this problem we will define the order of magnitude of both points, then we will obtain the radius and obtain the conclusion of the order of magnitude.
A nanosecond is one billionth of a second while and a millisecond is one millionth of a second
Therefore something that runs in nanoseconds is six times faster than something that runs in milliseconds