Physics · Kinetic Theory · NEET
Speed cannot be negative, so the curve must start at zero at v = 0. But there is no upper limit to speed, so a small number of molecules can have very high speeds. This creates a long tail on the right side. Because the right side stretches out further than the left, the curve is skewed, and the peak (most probable speed) sits to the left of the average speed.
The peak is the most probable speed, Vmp. It is the speed that the largest number of molecules have at that temperature. Formula: Vmp = square root of (2kT/m) = square root of (2RT/M). The peak is NOT the average speed and NOT the rms speed. Both of those lie to the right of the peak.
No. On the graph the order from left to right is always Vmp (the peak), then Vavg, then Vrms. Their ratio is fixed: Vmp : Vavg : Vrms = 1.00 : 1.13 : 1.22. So Vrms is always the largest and sits farthest to the right, never at the peak.
At higher temperature the whole curve shifts to the right (molecules move faster) and the peak becomes lower and broader (speeds spread out more). Important point: the total area under the curve stays the same because the total number of molecules does not change. Only the shape and position change.
The x-axis is molecular speed v. The y-axis is the number of molecules per unit speed range, often written dN/dv or the fraction f(v). The area under the curve between two speeds gives the number (or fraction) of molecules with speeds in that range. The total area equals the total number of molecules.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Most probable speed Vmp = square root of (2RT/M). Average speed Vavg = square root of (8RT/(pi M)). RMS speed Vrms = square root of (3RT/M). Here R is the gas constant, T is absolute temperature in kelvin, and M is molar mass in kg per mole.
It is square root of 2 : square root of (8/pi) : square root of 3, which is about 1.41 : 1.60 : 1.73, or normalized to 1.00 : 1.13 : 1.22. This ratio is the same for every gas at every temperature.
Yes. A lighter gas (smaller molar mass) has higher speeds, so its curve is shifted right and is flatter. A heavier gas at the same temperature peaks at a lower speed and is taller and narrower.
The area equals the total number of gas molecules. Heating the gas does not create or destroy molecules, so the area is fixed. Temperature only changes how the speeds are spread out.
Yes, it is part of Kinetic Theory of Gases. NEET usually asks the order of the three speeds, what the peak means, and how the curve changes with temperature, rather than a heavy numerical.
