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Problem 25 Medium Difficulty

An electron is in the second excited orbit of hydrogen, corresponding to $n=3 .$ Find (a) the radius of the orbit and (b) the wavelength of the electron in this orbit.

Answer

a) 0.476 $\mathrm{nm}$
b) 0.997 $\mathrm{nm}$

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

LB
Liev B.

Numerade Educator

Marshall S.

University of Washington

Aspen F.

University of Sheffield

Video Transcript

in this exercise, we have an electoral that is in the third energy level of the hydrogen atom. That is a second excited state and in question A. We have to find the radius of its orbit, and we know that the radius of the orbit of the end energy level in the hydrogen atom is given by and square times of more radius. A zero in this case and squared is nine and a zero is just separated. So that's 5.29 times into the miners. 11th meters. So are three. That's what we're looking for is equal to 4.76 times sent the minus 10 meters. Okay, in question be we have to calculate the wavelength off this electric. So for that, the first thing I'm gonna do is to calculate the linear momentum of the election. Remember that L the which is the angular momentum, can be written as the linear momentum times the radius. And since the Adam is in the Turk, the third energy level, this is able to three h bar. Okay, because the angular momentum is equal to end H bar. So the linear momentum is three h far divided by R. So this is three times aged, divided by two high. I am so three times 6.63 times 10 to the minus 34. You'll second divided by two times pi times the radius that we found in question A which is 4.76 time said to them anistan meters. So P is equal to six point sixties five times 10 to the minus 25 kilograms meters per second. Okay, And now if you want to calculate the wavelength London and remember that by the relief formal we have that London is equal to H over the momentum Age is 6.63 time sen to the minus 34 your second divided by the momentum. That's 6.65 time said to the minus 25 kilograms meters per second. So this is equal to 9.9 seven times 10 to the minus 10 meters. Okay, this is the wave going off the electric, But

Universidade de Sao Paulo
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

LB
Liev B.

Numerade Educator

Marshall S.

University of Washington

Aspen F.

University of Sheffield