First slide

Gravitaional potential energy

Question

At what temperature, hydrogen molecules will escape from the earth’s surface ? (Take mass of hydrogen molecule = 0.34 × 10^–6 kg, Boltzmann constant = 1.38 × 10^–23 KJ^–1, Radius of earth=6.4 × 10⁶m and acceleration due to gravity=9.8 ms^–2)

Moderate

A

10¹⁴ K
B

10² K
C

10²⁴ K
D

10⁴ K

Solution

$V_{r m s} = V_{e}; \sqrt{\frac{3 k T}{m}} = \sqrt{2 g R} T = \frac{2 m g R}{3 k}$
$T = \frac{2 \times 0.34 \times 10^{- 26} \times 9.8 \times 6.4 \times 10^{6}}{3 \times 1.38 \times 10^{- 23}} K$ = $10^{4}$ K

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