Question:
At \(300 K\) the rms speed of oxygen molecules is \(\sqrt {\frac {\alpha+5}{\alpha}}\) times to that of its average speed in the gas. Then, the value of \(\alpha\) will be
(used \(\pi=\frac {22}{7}\))
At \(300 K\) the rms speed of oxygen molecules is \(\sqrt {\frac {\alpha+5}{\alpha}}\) times to that of its average speed in the gas. Then, the value of \(\alpha\) will be
(used \(\pi=\frac {22}{7}\))
(used \(\pi=\frac {22}{7}\))
Updated On: Mar 25, 2026
- 28
- 24
- 32
- 27
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The root mean square (rms) speed and average speed are related as:
\[
\sqrt{\frac{3RT}{M}} = \frac{\alpha + 5}{\alpha} \sqrt{\frac{8RT}{\pi M}}
\]
Squaring both sides and simplifying:
\[
3 = \frac{\alpha + 5}{\alpha} \cdot \frac{8}{\pi}
\]
Substitute \(\pi = \frac{22}{7}\):
\[
3 = \frac{\alpha + 5}{\alpha} \cdot \frac{8 \times 7}{22}
\]
\[
3 = \frac{\alpha + 5}{\alpha} \cdot \frac{28}{22}
\]
\[
\alpha = 28
\]
Was this answer helpful?
0
0
Top JEE Main Physics Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88Ć106 nm-K. Then,
- $I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-
View More Questions
Top JEE Main Kinetic molecular theory of gases Questions
- What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?
Which statements are correct about degrees of freedom?
(A) A molecule with n degrees of freedom has n2 different ways of storing energy.
(B) Each degree of freedom is associated with (1/2)RT average energy per mole.
(C) A monatomic gas molecule has 1 rotational degree of freedom whereas diatomic molecule has 2 rotational degrees of freedom.
(D) CH4 has a total of 6 degrees of freedom.
Choose the correct answer from the option given below:
Top JEE Main Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
View More Questions
Concepts Used:
Kinetic Molecular Theory of Gases
Postulates of Kinetic Theory of Gases:
- Gases consist of particles in constant, random motion. They continue in a straight line until they collide with each other or the walls of their container.
- Particles are point masses with no volume. The particles are so small compared to the space between them, that we do not consider their size in ideal gases.
- Gas pressure is due to the molecules colliding with the walls of the container. All of these collisions are perfectly elastic, meaning that there is no change in energy of either the particles or the wall upon collision. No energy is lost or gained from collisions. The time it takes to collide is negligible compared with the time between collisions.
- The kinetic energy of a gas is a measure of its Kelvin temperature. Individual gas molecules have different speeds, but the temperature and
kinetic energy of the gas refer to the average of these speeds. - The average kinetic energy of a gas particle is directly proportional to the temperature. An increase in temperature increases the speed in which the gas molecules move.
- All gases at a given temperature have the same average kinetic energy.
- Lighter gas molecules move faster than heavier molecules.
