At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at -20 °C ? (Atomic mass of Ar = 39 u and He = 400 u)

Question

At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at -20 °C ? (Atomic mass of Ar = 39 u and He = 400 u) (A) 2.52 × 103 K (B) 2.52 × 102 K (C) 4.03 × 103 K (D) 4.03 × 102 K

Tardigrade Admin · Accepted Answer

Let 1 and 2 represent for Argon atom and Helium atom. rms speed of Argon, vrms1 = √(3RT1/M1) rms speed of Helium, vrms2 = √(3RT2/M2) According to question, Vrms1 = Vrms2 ∴ √(3RT1/M1) = √(3RT2/M2), (T1/M1) = (T2/M2) or T1 = (T2/M2) × M1 = (253/4) ×39.9 = 2.52 ×103 K

Q. At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at - $20^{\circ} C$ ? (Atomic mass of $A r = 39 u$ and $He = 400 u$ )

$2.52 \times 1 0^{3} K$

$2.52 \times 1 0^{2} K$

$4.03 \times 1 0^{3} K$

$4.03 \times 1 0^{2} K$

Q. At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at -20∘C ? (Atomic mass of Ar=39u and He=400u)

2.52×103K

2.52×102K

4.03×103K

4.03×102K

Q. At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at - $20^{\circ} C$ ? (Atomic mass of $A r = 39 u$ and $He = 400 u$ )

$2.52 \times 1 0^{3} K$

$2.52 \times 1 0^{2} K$

$4.03 \times 1 0^{3} K$

$4.03 \times 1 0^{2} K$