Question

The r.m.s velocity of hydrogen at ${27^ \circ }C$, R = $8.314$ ${\text{J mo}}{{\text{l}}^{ - 1}}{K^{ - 1}}$ is
A.$1.934{\text{ m}}{{\text{s}}^{ - 1}}$
B.$19.34{\text{ m}}{{\text{s}}^{ - 1}}$
C.$193.4{\text{ m}}{{\text{s}}^{ - 1}}$
D.$1934{\text{ m}}{{\text{s}}^{ - 1}}$

Answer 1

Velocity is defined as the rate of change of position of an object with respect to a frame of reference and is a function of time. Its SI unit is meter per second. The formula is given below. We shall just substitute the value to calculate the velocity.
Formula used:
${U_{RMS}} = \sqrt {\dfrac{{3RT}}{{{M_W}}}}$
Where R is a constant, T is the temperature, ${M_w}$ is the molecular weight and U is the r.m.s. velocity.

Complete step by step answer:
Hydrogen is the chemical element with the symbol H. Its atomic number is 1. Hydrogen is the lightest element out of all the known elements of the periodic table. Hydrogen is the most abundant chemical substance in the universe. Most common isotope of hydrogen is termed as protium; it has one proton and no neutron. Some of the other isotopes of hydrogen are,
Deuterium
Tritium
Hydrogen-1
Helium-3
Hydrogen-4
Hydrogen-5
The gas constant also referred to as the molar gas constant, universal gas constant, or perfect gas constant and is denoted by the symbol R. It's like the Boltzmann constant, but expressed in units of energy per temperature increment per mole, that is the pressure–volume product, instead of energy per temperature increment per particle. The constant is additionally a mixture of the constants from Boyle's law, Gay-Lussac's law, Avogadro's law, and Gay-Lussac's law. It's a physical constant that's featured in many fundamental equations within the physical sciences, like the ideal gas law, the Arrhenius equation, and the Nernst equation.
As we know,
${U_{RMS}} = \sqrt {\dfrac{{3RT}}{{{M_W}}}}$
${U_{RMS}} = \sqrt {\dfrac{{3 \times 8.314 \times 300}}{{2 \times {{10}^{ - 3}}}}}$
${U_{RMS}} = 1934{\text{m/s}}$

Here, the correct option is D as the correct answer is 1934 ${\text{m}}{{\text{s}}^{ - 1}}$.

Note:
The root mean square (RMS or rms) is defined as the root of the mean square. The RMS may be additionally referred to as the quadratic mean and is a particular case of the generalized mean with exponent.