At 300K what is the rms speed of Helium atom?[ mass of He atom is 4u,

1.	At 300K what is the rms speed of Helium atom?[ mass of He atom is 4u, 1u = 1.66 x 10-27 kg, kB = 1.38 x 10-23J/K]
Answer» Answer:- $\red{\bigstar}$ $\large\leadsto\boxed{\sf \green{1368 \: m/s}}$ • Given:- Temperature [T] = 300 K Mass of He atom = 4U Boltzmann constant [KB] = 1.38 × 10-²³ J/K • Solution:- $\pink{\bigstar}$ $\boxed{\sf \red{v_{<klux>RMS</klux>} = \sqrt{\dfrac{3k_{B}T}{m}} = \sqrt{\dfrac{3RT}{M_{m}}}}}$ where, $\sf{\dfrac{M_{m}}{m} = \dfrac{R}{kB}}$ here, kB = Boltzmann constant T = Temperature M = MOLAR mass m = mass of gas in kg R = Universal Gas constant Hence, $\pink{\bigstar}$ $\boxed{\sf \red{v_{RMS} = \sqrt{\dfrac{3RT}{M_{m}}}}}$ TAKING:- R = 8.314472 J/mol. K T = 300 K Mm = 4.0026 × 10-³ kg/mol. → $\sf \sqrt{\dfrac{3 (8.314472 J/mol.K) 300 K}{4.0026 \times 10^{-3} kg/mol}}$ → $\sf \sqrt{\dfrac{7483.0248}{4.0026 \times 10^{-3} kg/mol}}$ → $\sf{\sqrt{1869.540998 \times 10^{3} kg/mol}}$ → $\sf{\sqrt{1869540.998}}$ → $\sf{1367.311595}$ Therefore, the rms speed of He is 1367.311595 ≈ 1368 m/s.