Question

At what temperature will he atom have the same $rms$ speed as $H_2$ molecules have at ${27}^{0}C$ ?

• A. ${127}^{0}C$
• B. ${227}^{0}C$
• C. ${327}^{0}C$
• D. ${27}^{0}C$

Answer 1

Answer: (C)

${327}^{0}C$

$V_{rms}=\sqrt{\frac{3RT}{M}}\Rightarrow \sqrt{\frac{3{RT}_1}{M_{He}}}=\sqrt{\frac{{3RT}_2}{M_{H_2}}}$

Given $T_1={27}^{0}C=300K$

$\frac{T_1}{T_2}=\frac{M_{He}}{M_{H_2}}\Rightarrow T_1=T_2\times \frac{M_{He}}{M_{H_2}}$

$=300\times \frac{4}{2}=600K$

$T_2=600-273={327}^{0}C$