Question:
Which of the following relation is correct? (\(v_{\mathrm{rms}}\): root mean square velocity, \(\bar{v}\): mean velocity and \(v_{\mathrm{mp}}\): most probable velocity)
Which of the following relation is correct? (\(v_{\mathrm{rms}}\): root mean square velocity, \(\bar{v}\): mean velocity and \(v_{\mathrm{mp}}\): most probable velocity)
Show Hint
Remember the order: RMS \(>\) Average \(>\) Most probable.
Updated On: Apr 16, 2026
- \( v_{\mathrm{rms}}>\bar{v}<v_{\mathrm{mp}} \)
- \( v_{\mathrm{rms}} v_{\mathrm{mp}} \)
- \( v_{\mathrm{rms}}>\bar{v}>v_{\mathrm{mp}} \)
- None of these
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
For Maxwell–Boltzmann distribution: \[ v_{\mathrm{rms}} = \sqrt{\frac{3kT}{m}}, \quad \bar{v} = \sqrt{\frac{8kT}{\pi m}}, \quad v_{\mathrm{mp}} = \sqrt{\frac{2kT}{m}} \] Compare magnitudes \[ \sqrt{3}>\sqrt{\frac{8}{\pi}}>\sqrt{2} \] \[ \Rightarrow v_{\mathrm{rms}}>\bar{v}>v_{\mathrm{mp}} \]
For Maxwell–Boltzmann distribution: \[ v_{\mathrm{rms}} = \sqrt{\frac{3kT}{m}}, \quad \bar{v} = \sqrt{\frac{8kT}{\pi m}}, \quad v_{\mathrm{mp}} = \sqrt{\frac{2kT}{m}} \] Compare magnitudes \[ \sqrt{3}>\sqrt{\frac{8}{\pi}}>\sqrt{2} \] \[ \Rightarrow v_{\mathrm{rms}}>\bar{v}>v_{\mathrm{mp}} \]
Was this answer helpful?
0
0
Top MET Physics Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- A rope of mass $0.1\, kg$ is connected at the same height of two opposite walls. It is allowed to hang under its own weight. At [he contact point between the rope and the wall, the rope makes an angle $ \theta =10^{\circ} $ with respect to horizontal. The tension in the rope at its midpoint between the walls is
- At great distances from an electric dipole, the electric field strength due to the dipole varies with the distance as
View More Questions
Top MET kinetic theory Questions
- If the rms velocity of a gas is v, then
- If one mole of monoatomic gas (\(\gamma = \frac{5}{3}\)) is mixed with one mole diatomic gas (\(\gamma = \frac{7}{5}\)), the value of \(\gamma\) for the mixture is:
- Ideal gas insulated, heated by current through resistance \(100\Omega\), current \(1A\) for 5 min. Find change in internal energy.
Top MET Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- Which of the following product is formed in the reaction $ CH_3MgBr {->[(i)CO_2][(ii)H_2O]} ? $
View More Questions