Consider a sample of oxygen behaving like an ideal gas. At \(300 \,K ,\) the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be : (Molecular weight of oxygen is \(32 \,g / mol\) \(\left. R =8.3 \,J K ^{-1} mol ^{-1}\right)\)

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(C) \(\sqrt{\frac{3 \pi}{8}}\)

Step-by-step Solution

Detailed explanation

\(v _{vms }=\sqrt{\frac{3 RT }{ M }}\)

\(v _{ avg }=\sqrt{\frac{8 RT }{\pi} \frac{ RT }{ M }}\)

\(\frac{ v _{ rms }}{ v _{ avg }}=\sqrt{\frac{3 \pi}{8}}\)

Same subject

A person pushes a box on a rough horizontal platform surface. He applies a force of \(200\, N\) over a distance of \(15\, m .\) Thereafter, he gets progressively tired and his applied force reduces linearly with distance of \(100\, N\). The total distance through which the box has been moved is \(30\, m\). What is the work done by the person during the total movement of the box\(........J\)\(?\)

JEE Mains 2020 Hard
The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively \(1.5\%\) and \(1\%\), the maximum error in determining the density is ........ \(\%\)

JEE Mains 2018 Easy
An electric charge \(10^{-6} \mu \mathrm{C}\) is placed at origin \((0,0)\) \(\mathrm{m}\) of \(\mathrm{X}-\mathrm{Y}\) co-ordinate system. Two points \(\mathrm{P}\) and \(\mathrm{Q}\) are situated at \((\sqrt{3}, \sqrt{3}) \mathrm{m}\) and \((\sqrt{6}, 0) \mathrm{m}\) respectively. The potential difference between the points \(P\) and \(Q\) will be :

JEE Mains 2024 Hard
An \(LCR\) circuit as shown in the figure is connected to a voltage source \(V_{ac}\) whose frequency can be varied. The frequency, at which the voltage across the resistor is maximum, is......\(Hz\)

JEE Mains 2013 Easy
A parallel plate capacitor with plates of area \(1\,m^2\) each, are at a separation of \(0.1\,m.\) If the electric field between the plates is \(100\,N/C,\) the magnitude of charge on each plate

JEE Mains 2019 Medium
If the collision frequency of hydrogen molecules in a closed chamber at \(27^{\circ} \mathrm{C}\) is \(\mathrm{Z}\), then the collision frequency of the same system at \(127^{\circ} \mathrm{C}\) is _______.

JEE Mains 2024 Hard

Explore more questions on app

From JEE Mains

At what distance above and below the surface of the earth a body will have same weight? (take radius of earth as \(R\).)

JEE Mains 2024 Hard
A particle executes simple harmonic motion and is located at \(x = a, b\) and \(c\) at times \(t_0, 2t_0\) and \(3t_0\) respectively. The frequency of the oscillation is

JEE Mains 2018 Hard
A particle \(A\) of mass \(‘m’\) and charge \(‘q’\) is accelerated by a potential difference of \(50\, V\). Another particle \(B\) of mass \(‘4\, m’\) and charge \(‘q’\) is accelerated by a potential difference of \(2500\, V\). The ratio of de-Broglie wavelength \(\frac{{{\lambda _A}}}{{{\lambda _B}}}\) is close to

JEE Mains 2019 Medium
In a Young's double slit experiment, the separation between the slits is \(0.15\; \mathrm{mm}\). In the experiment, a source of light of wavelength \(589 \;\mathrm{nm}\) is used and the interference pattern is observed on a screen kept \(1.5\; \mathrm{m}\) away. The separation between the successive bright fringes on the screen is......\(mm\)

JEE Mains 2020 Medium
The escape velocity of a body on a planet \('A'\) is \(12 \,kms ^{-1}\). The escape velocity of the body on another planet \('B'\) , whose density is four times and radius is half of the planet \('A'\), is ................... \(kms ^{-1}\)

JEE Mains 2022 Medium

Explore more questions on app