Maxwell's Distribution of Speeds

Q.

What is the relation between RMS velocity, average velocity, and most probable velocity?

Q.

What is the average translational kinetic energy of molecules in an ideal gas at $37°\mathrm{C}$?

Q. The average velocity at $T_{1}K$, and the most probable velocity at $T_{2}K$ of $C{O}_2$ gas is $9.0\times {10}^4{\text{cm sec}}^{-1}$. The value of $T_1$ is K and $T_2$ is K.

Q. Which one of the following statements is NOT true about the effect of an increase in temperature on the distribution of molecular speeds in a gas

1. The most probable speed increases
2. The area under the distribution curve remains the same as under the lower temperature
3. The fraction of the molecules with the most probable speed increases
4. The distribution becomes broader

Q. The correct order of molecular velocities is $u_{mp}<u_{av}<u_{rms}$

1. False
2. True

Q. The ratio of $u_{\text{avg}}$ and $u_{\text{rms}}$ of a gas at a particular temperature is

1. 1.1086 : 1
2. 0.92 : 1
3. 1 : 1.1086
4. 1:0.92

Q. The average velocity at $TK$ of $C{O}_2$ gas is $9.0\times {10}^4{\text{cm sec}}^{-1}$. The value of $T$ is______.

Q.

Calculate the radius of the nth orbit

1. $\sqrt{\frac{\mathrm{nh}}{2\mathrm{\pi eB}}}$

2. $\sqrt{\frac{\mathrm{nheB}}{2\mathrm{\pi }}}$

3. $\sqrt{\frac{\mathrm{nhe}}{2\mathrm{\pi B}}}$

4. $\sqrt{\frac{\mathrm{nhB}}{2\mathrm{\pi e}}}$

Q.

A potential difference of $20\mathrm{kV}$ is applied across an X-ray tube. The minimum wavelength of X-rays generated is ____________ ${\mathrm{A}}^{\circ }$.

1. $1.621\mathrm{A}°$

2. $0.621\mathrm{A}°$

3. $2.621\mathrm{A}°$

4. $5.621\mathrm{A}°$

Q.

The average molecular speed is the greatest in which of the following gas samples?

1. of at

2. of at

3. of at

4. of at

Q. The lowest energy X-rays having $\lambda =3.055\times {10}^{-8}m$. Which of the following statements is/are true?

1. The minimum difference in energy between two Bohr's orbits such that an electronic transition would correspond to the emission of an X-ray is $6.52\times {10}^{-18}J$
2. For $Z=2$ the transiton that corresponds to the above radiation is $n=2$ to $n=1$
3. For $Z=2$ the transiton that corresponds to the above radiation is $n=3$ to $n=2$
4. The minimum difference in energy between two Bohr's orbits such that an electronic transition would correspond to the emission of an X-ray is $1.65\times {10}^{18}J$

Q. Equal time is taken by 100 ml hydrogen and 25 ml of a gas to diffuse through a porous partition.Calculate the molecular weight of the gas.

1. 23 gm
2. 32 gm
3. 64 gm
4. 46 gm

Q. The correct statement about probability density (except at infinite distance from nucleus) is

1. It can never be zero for 2s orbital
2. It can be zero for 3p orbital
3. It can be zero for 1s orbital
4. It can be negative for 2p orbital

Q.

Compare the energy released during direct electronic transition from 4^th orbit to 1^st orbit with the energy released during successive electronic transitions between the same orbits in H-atom. Is the energy of all successive transitions between the 4^th orbit and 1^st orbit equal?

Q. Assertion :The area under the Maxwell distribution molecular speed curve remains same irrespective of the temperature of the gas. Reason: The fraction of molecules with most probable speed increases with the increase of temperature.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect but Reason is correct

Q.

If the absolute temperature of a sample of gas in a fixed volume container is quadrupled, then the root mean square speed in the initial state $U_i$ and that in the final state $U_f$ would be related as :

1. 

2. 

3. 

4. 

Q. Which of the following is not correct in relevance to Maxwell's Distribution curve?

1. On increasing the temperature, the fraction of molecules having lower speed (range) increases
2. Majority of molecules have speed almost equal to most probable speed
3. Speed distribution also depends on the molar mass of the gas
4. Total area under the curve is a measure of the total number of molecules

Q. Assertion :In maxwell distribution curve, with increase in temperature the fraction of molecules possessing most probable velocity increases. Reason: With increasing temperature molecular velocities increases.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect but Reason is correct

Q. In the following graph of Maxwell-Boltzmann distribution of molecular velocities

Which of the following is the correct order of temperature?

1. $T_1<T_2<T_3$
2. $T_3<T_2<T_1$
3. $T_2<T_1<T_3$
4. None

Q. If k is the Boltzmann constant, the average kinetic energy of a gas molecule at absolute temperature T is?

Q. Given is the graph of Maxwell-Boltzmann distribution of molecular velocities.


Which of the option is correct?

1. $T_1<T_2<T_3$
2. $T_3<T_2<T_1$
3. $T_2<T_1<T_3$
4. $T_2<T_1=T_3$

Q.

Which one of the following statements in NOT true about the effect of an increase in temperature on the distribution of molecular speeds in a gas?

1. The distribution becomes broader

2. The area under the distribution curve remains the same as under the lower temperature

3. The fraction of the molecules with the most probable speed increases

4. The most probable speed increases

Q. The average velocity at $TK$ of $C{O}_2$ gas is $9.0\times {10}^4{\text{cm sec}}^{-1}$. The value of $T$ is______.

Q.

Give the dimensional formula for Boltzmann’s constant.

Q. A longer, wider, and symmetrical Maxwell-Boltzmann distribution suggest which of the following?

1. Most of the molecules being examined have the same speed
2. There is a wide distribution of speeds among the molecules being examined.
3. There is a greater proportion of molecules with a high speed than with a low speed.
4. There is a greater proportion of molecules with a low speed than with a high speed.

Q.

Which one of the following statement(s) is/are not true about the effect of an increase in temperature on the distribution of molecular speeds in a gas?

1. The most probable speed increases.

2. The fraction of the molecules with the most probable speed increases.

3. The distribution becomes broader.

4. The area under the distribution curve remains the same as under the lower temperature.

Q.

Among the following gases which one has the lowest root mean square velocity at 25${}^{\circ }$ C

1. $S{O}_2$

2. $N_2$

3. $O_2$

4. $C{L}_2$

Q. Which of the following statements about Maxwell-Boltzmann law of distribution of molecular speeds are correct?

1. The fraction of molecules having speed between c and $(c+dc)$ (regardless of direction) is given by: $4\pi {\left(\frac{M}{2\pi RT}\right)}^{3/2}{c}^{2}exp\left(\frac{M{c}^2}{2RT}\right)dc$.
2. The speed distribution function is used to determine average molecular speeds.
3. The speed distribution curve becomes sharper and is more peaked at a higher temperature as the average speed increases.
4. The average speed is the arithmetic mean of the different speeds of all the molecules present in a given sample of the gas.

Q. Two 1 liter flasks contain hydrogen and oxygen, respectively, at the same temperature and pressure. It is true that the hydrogen and oxygen molecules have the same average
(1) kinetic energy
(2) mass
(3) speed

1. If 1, 2 and 3 are correct
2. If only 1 and 2 are correct
3. If only 2 and 3 are correct
4. If only 1 is correct
5. If only 3 is correct

Q. Which one of the following statements is $not$ true about the effect of the increase in temperature on the distribution of molecular speeds in gases?

1. The area under the distribution curve remains the same as under the lower temperature.
2. The distribution becomes broader
3. The fraction of the molecules with the most probable speed increases
4. The most probable speed increases