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Problem 54 Hard Difficulty

Review problem. (a) How much energy is required to cause an electron in hydrogen to move from the $n=1$ state to the $n=2$ state? (b) Suppose the atom gains this energy through collisions among hydrogen atoms at a high temperature. At what temperature would the aver- age atomic kinetic energy 3$k_{B} T / 2$ be great enough to excite the electron? Here $k_{B}$ is Boltmann's constant.

Answer

a. 10.2 $\mathrm{eV}=1.63\times10^{-18} \mathrm{J}$
b. $T=7.88\times10^4 \mathrm{K}$

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Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

Farnaz M.

Simon Fraser University

Zachary M.

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Jared E.

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Video Transcript

to find he amount of energy required to excite electron from Khost. Want to accustom to ust Christian right? Where the energy state or the energy off the any any energy level and for hydrogen atom is given s negative 13.6 p divided by N square. So the energy quiet Taayie to move from any close to want Americans to just take me to my next one. This is, uh, 13.6 feet. Type I one minus to square. 10 days would give us 10.2 even which is, if we are to call ready to juice, multiply this by 1.6% Apartments 19. We should get about 1.6 tree stand off minus 18 Jokes Not to find the temperature at which the surrounding atoms will have enough kinetic energy to excite the electron. You mean instead, uh, kinetic energy? This goes to the delta and by the ECRI petition. Terram, we know that this kinetic energy is going even a strip or two k p t Kibby steeple expense constant. So temperature justic delta v Times foot Obaidi boats Men constant already bought, spends constant. Yes, witness 1.38 tent Pole minister treat. All right, so substituting dot i e putting you to co creator. We should. That's about seven point. It eats some sent off for Kelvin's.

National University of Singapore
Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

Farnaz M.

Simon Fraser University

Zachary M.

Hope College

Jared E.

University of Winnipeg