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Problem 11 Medium Difficulty

A hydrogen atom is in its first excited state $(n=2)$. Using the Bohr theory of the atom, calculate (a) the radius of the orbit, (b) the linear momentum of the electron, (c) the angular momentum of the electron, (d) the kinetic energy, (e) the potential energy, and (f) the total energy.

Answer

a) 0.212 $\mathrm{nm}$
b) $9.95 \times 10^{-25} \mathrm{kg} . \mathrm{m} / \mathrm{s}$
c)$2.11 \times 10^{-34} \frac{\mathrm{Kg} \mathrm{m}^{2}}{5}$
d) $5.44 \times 10^{-19} \mathrm{~J}$
e)$-10.87 \times 10^{-19} \mathrm{~J}$
f)$-5.43 \times 10^{-19} \mathrm{~J}$

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Aspen F.

University of Sheffield

Video Transcript

in this exercise, we have an Adam at its second energy level. And in the first question, we have to calculate the radius on the orbit s so we know that the radius is and squared times aboard radius. So this is four times of a radius since and equals two. And this is four times 5.29 times into the mine, his 11th. That's the Bradys. So this is two times 2.12 times sent to the minus 10 meters. Okay, in question be we have to calculate the linear momentum of the electric. And so this is what we want to calculate. P. Notice that the angular momentum l is going ties and is given by N times H Bar. We also know that billionaire Mo Mentum is equal to p. The linear moment sometimes are. So we have that the billionaire mo mentum is age. I'm sorry. Ah and h bar divided by r So this is to times two times h over two pi That's each bar divided by and this is age over pie are so we can calculate it explicitly. Age is 6.63 times 10 to the minus 34 usual second divided by pi. Times are and are, as we calculated in the question they is 2.12 times 10 to the minus 10 meters. So the linear momentum is nine 0.95 times 10 to the minus 25 kilograms meters per second. Okay, in question. See, we have to calculate the angular momentum and that's just ah and pie. I'm sorry in H bar. So this is two times H over too high, which is a church over pie. So this is 6.63 times sent to the minors. 34 you'll second divided by pi which if 2.11 times 10 to the minus 34 kilograms kilograms meters square for a second. When you just ride the second here, little better second okay in question. Do you have to calculate the kinetic energy? The kinetic energy is equal to the leaner moment I'm squared over two times the mass. So this is what we already calculated the the linear momentum. That's 9.95 times 10. The minus 25th squared this in kilograms square meters squared per second squared, divided by two times the mass of the electron, which is 9.1 time to send to the minus 31 kilograms. So K is equal to 5.44 times 10 to the minus 19 jewels in question e, we have to calculate the potential energy potential. Energy is equal to k times the charge of the election, which is mine. A z times a charge of the program, which is he just plus e so minus K e squared, divided by the radius. So this is minus nine time. State of the nine Newtons meters squared Curriculum square times 1.6 times 10 to the miners, 19 10th Coombs Squared, divided by r and R as a complicated in question one is two points. 12 question. They actually two point 12 times since the A minus 10 meters. So you is able to minus 10 point 87 times 10 to the minus 19. You'll finally in question after we have to calculate the total energy, and that's just gonna be the Connecticut where you plus the potential energy. So this is, uh, minus 10.87. Maybe so, plus 5.44 time sent to the minus 19. So e equals minus 5.43. Time stand in the minors, 19th fuels and this is the end over exercise.

Universidade de Sao Paulo
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Aspen F.

University of Sheffield