The first excited state of a hydrogen atom is | vedclass

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(C) The energy required to excite the hydrogen atom to the first excited state is $\Delta E = 10.2 \ eV$.To find the temperature $T$,we equate the ave

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$7.88 	imes 10^4 \ K$

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(C) The energy required to excite the hydrogen atom to the first excited state is $\Delta E = 10.2 \ eV$.To find the temperature $T$,we equate the average kinetic energy of the gas atoms to the excitation energy: $\frac{3}{2} kT = \Delta E$.Here,$k = 1.38 	imes 10^{-23} \ J/K$ is the Boltzmann constant and $\Delta E = 10.2 	imes 1.6 	imes 10^{-19} \ J$.Substituting the values: $T = \frac{2 \Delta E}{3k} = \frac{2 	imes 10.2 	imes 1.6 	imes 10^{-19}}{3 	imes 1.38 	imes 10^{-23}}$.$T = \frac{32.64 	imes 10^{-19}}{4.14 	imes 10^{-23}} \approx 7.88 	imes 10^4 \ K$.

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

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