JEE Mains · Physics · STD 11 - Kinetic theory of gases
- JEE Mains 2019
- Medium
- MCQ
The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth is closest to : [Boltzmans Constant \(k_B = 1.38\times10^{-23}\, J / K\) Avogadro number \(N_A = 6.02\times10^{26}\, / kg\) Radius of Earth \(: 6.4\times10^6\, m\) Gravitation acceleration on Earth \(= 10\, ms^{-2}\)]
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(10^4\,K\)
Step-by-step Solution
Detailed explanation
\(v_{m s}=\sqrt{\frac{3 R T}{m}} \quad v_{\text {escape }}=\sqrt{2 g R_{e}}\)
\(\mathrm{v}_{\mathrm{rms}}=\mathrm{v}_{\text {escape }}\)
\(\frac{3 \mathrm{RT}}{\mathrm{m}}=2 \mathrm{gR}_{\mathrm{e}}\)
\(\frac{3 \times 1.38 \times 10^{-23} \times 6.02 \times 10^{26}}{2} \times 10 \times 10^{3}=10^{4} \mathrm{k}\)
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