वह तापमान, जिस पर हाइड्रोजन अणु का वर्ग माध्य मूल वेग, पृथ्वी से उसके पलायन वेग के बराबर होगा, का सन्निकट मान है : [दिया है : बोल्टजमॉन नियतांक \(k _{ B }=1.38 \times 10^{-23} \,J / K,\) आवोगाद्रो संख्या \(N _{ A }=6.02 \times 10^{26} \, / kg,\) पृथ्वी की त्रिज्या : \(6.4 \times 10^{6} \,m,\) पृथ्वी पर गुरुत्वीय त्वरण \(=10 \,ms ^{-2}\) ]

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.