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(A) According to the kinetic theory of gases,the average kinetic energy of a gas molecule at temperature $T$ is given by $E = \frac{3}{2} kT$,where $k

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$7.9 	imes 10^4 \, K$

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(A) According to the kinetic theory of gases,the average kinetic energy of a gas molecule at temperature $T$ is given by $E = \frac{3}{2} kT$,where $k$ is the Boltzmann constant $(k = 1.38 	imes 10^{-23} \, J/K)$.To excite a hydrogen atom to the first excited state,the kinetic energy of the colliding particles must be at least $10.2 \, eV$.Converting the energy to Joules: $E = 10.2 	imes 1.6 	imes 10^{-19} \, J = 1.632 	imes 10^{-18} \, J$.Equating the energy: $1.632 	imes 10^{-18} = \frac{3}{2} 	imes (1.38 	imes 10^{-23}) 	imes T$.Solving for $T$: $T = \frac{1.632 	imes 10^{-18} 	imes 2}{3 	imes 1.38 	imes 10^{-23}} \approx 7.88 	imes 10^4 \, K$.Rounding to the nearest given option,$T \approx 7.9 	imes 10^4 \, K$.

The first excited state of a hydrogen atom is $10.2 \, eV$ above its ground state. The temperature needed to excite hydrogen atoms to the first excited level is

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