Question

For a monatomic gas, kinetic energy is $E$. The relation of E with rms velocity is

• A. $u_{rms}={\left(\frac{2E}{m}\right)}^{\frac{1}{2}}$
• B. $u_{rms}={\left(\frac{3E}{2m}\right)}^{\frac{1}{2}}$
• C. $u_{rms}={\left(\frac{E}{2m}\right)}^{\frac{1}{2}}$
• D. $u_{rms}={\left(\frac{E}{3m}\right)}^{\frac{1}{2}}$

Answer 1

The correct option is A $u_{rms}={\left(\frac{2E}{m}\right)}^{\frac{1}{2}}$

Kinetic energy $\left(E\right)=\frac{3}{2}kT$.......(i)
RMS speed $\left(u_{rms}\right)=\sqrt{\frac{3kT}{m}}$.......(ii)
Multiply and divide 2 in equation (ii)
RMS speed $\left(u_{rms}\right)=\sqrt{\frac{3kT\times 2}{m\times 2}}....\left(iii\right)$
Substituting equation (ii) in (iii) we get,
$\Rightarrow u_{rms}=\sqrt{\frac{2E}{m}}$