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Review. (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 average atomic kinetic energy $\frac{3}{2} k_{\mathrm{B}} T$ be great enough to excite the electron? Here $k_{\mathrm{B}}$ is Boltzmann's constant.

a) 10.2 $\mathrm{eV}$

b) $7.88 \times 10^{4} \mathrm{K}$

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Cornell University

University of Michigan - Ann Arbor

Hope College

University of Winnipeg

to figure how much energy is required to lift the electron from the in equals one. So in survive, the initial is equal to one to the final state and Sabbeth being equal to two. We use the fact that the energy is equal to the ground. State energy 13.6 TV times thedc trained one over the initial state squared minus one of the final state in the transition squared is this would be 1/1 squared, minus 1/2 squared. Carrying out this operation, we find that this comes out people 10.2 electron volts, which is our answer to car A. But we notice in part B, we have we're trying to solve for the temperature t using the Bolton Constant, which has s I units. So we want to convert from electron volts to Jules. There's 1.6 times 10 to the minus 19. Jewell and everyone electron bulk. So this comes out to equal 1.63 times 10 to the minus 18. Jules, both are correct, so we can go ahead and box both of them and as a solution for part A. But we're gonna use the jewels version as our value for part B when it comes to solving for the temperature. So now all we have to do is solve for T when we find that T is gonna be equal to the swear root of two times the energy which we found in part a divided by the bulls names constant case of B again. We're using the jewels version of energy. This gives us a value in units of Kelvin's. So this comes out to equal 7.88 times, 10 to the four Kelvin.

University of Kansas