The respective speeds of the molecules are 1, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The root mean square velocity $(v_{rms})$ is given by the formula: $v_{rms} = \sqrt{\frac{v_1^2 + v_2^2 + v_3^2 + v_4^2 + v_5^2}{n}}$.Substituting

Vedclass · Accepted Answer

$\sqrt{11} : 3$

Vedclass · Answer

(A) The root mean square velocity $(v_{rms})$ is given by the formula: $v_{rms} = \sqrt{\frac{v_1^2 + v_2^2 + v_3^2 + v_4^2 + v_5^2}{n}}$.Substituting the given values: $v_{rms} = \sqrt{\frac{1^2 + 2^2 + 3^2 + 4^2 + 5^2}{5}} = \sqrt{\frac{1 + 4 + 9 + 16 + 25}{5}} = \sqrt{\frac{55}{5}} = \sqrt{11} \ km/s$.The average velocity $(v_{av})$ is given by the formula: $v_{av} = \frac{v_1 + v_2 + v_3 + v_4 + v_5}{n}$.Substituting the given values: $v_{av} = \frac{1 + 2 + 3 + 4 + 5}{5} = \frac{15}{5} = 3 \ km/s$.The ratio of $v_{rms}$ to $v_{av}$ is $\frac{\sqrt{11}}{3}$,which is $\sqrt{11} : 3$.

The respective speeds of the molecules are $1, 2, 3, 4$ and $5 \ km/sec$. The ratio of their $r.m.s.$ velocity and the average velocity will be

Similar Questions

The root mean square velocity of a gas molecule of mass $m$ at a given temperature is proportional to

The root mean square speed of hydrogen molecules of an ideal hydrogen gas kept in a gas chamber at $0^{\circ}C$ is $3180 \ m/s$. The pressure on the hydrogen gas is ..... $atm$ (Density of hydrogen gas is $8.99 \times 10^{-2} \ kg/m^3$,$1 \ atm = 1.01 \times 10^5 \ N/m^2$).

The temperature at which the root mean square speed of a gas will be half of its value at $0\,^{\circ}C$ is ....... $^{\circ}C$.

The root mean square velocity of the molecules in a sample of helium is $(5/7)^{th}$ that of the molecules in a sample of hydrogen. If the temperature of the hydrogen sample is $0^{\circ}C$,then the temperature of the helium sample is about:

If the root mean square velocity of the molecules of hydrogen at $NTP$ is $1.84 \, km/s$,calculate the root mean square velocity of oxygen molecule at $NTP$. The molecular weights of hydrogen and oxygen are $2$ and $32$ respectively.

Vedclass Test Series

Exam Paper Generator

Online Exam Module