The temperature at which oxygen molecules have the same root mean...

The temperature at which oxygen molecules have the same root mean square speed as helium atoms have at 300 K is : (Atomic masses : He = 4 u, O = 16 u)

Options

A600 K
B2400 K
C1200 K
D300 K

Correct answer

B. 2400 K

Step-by-step solution

{\text{C}}_{\text{rms}} = \sqrt{\dfrac{3 \text{RT}}{\text{M}}}

{\left({\text{C}}_{\text{rms}}\right)}_{\text{He}} = \sqrt{\dfrac{3 \text{R} \times 3 0 0}{4}}

{\left({\text{C}}_{\text{rms}}\right)}_{{\text{O}}_{2}} = \sqrt{\dfrac{3 \text{R} \times {\text{T}}_{{\text{O}}_{2}}}{3 2}}

∴ {( {C}_{rms} )}_{He} = {( {C}_{rms} )}_{{O}_{2}} ⇒ \dfrac{3R \times 300}{4} = \dfrac{3R \times {T}_{{O}_{2}}}{32}

{\text{T}}_{{\text{O}}_{2}} = \dfrac{3 0 0 \times 3 2}{4} = 2 4 0 0 K

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