Optics B/C

[hexagonaria]

So regionals was yesterday. We were in optics doing the laser shoot. It turns out that those proctors didn't know how to properly secure the laser to the table or mount mirrors properly. The mirrors has magnets on the back, and were stuck to L-shaped iron thingys. The first time 'round, the laser was going exactly as it should have been, except the third mirror was apparently jacked up and angled slightly down, so the laser his the floor of the box. It was on the line that I traced out on the template exactly as the laser should have been going. If that mirror hadn't been angled down, the laser might have hit with an accuracy of 5 +/- 3 mm. So, we had to redo the whole thing with the mirrors pasted to the other side of the L-shaped iron thingys, and because the bottom of the L-shaped thingys were protruding out in front of the mirror itself, the laser completely missed the fourth mirror and ended up hitting the wrong wall of the box. Also, the block that the laser mounted to was secured to the table with 8 pieces of masking tape (aka, the least adhesive tape there is out there).
We placed 3rd, after two of the teams that we coached...what a failure...

That would be frustrating! My sympathies are with you sir.
But really, bronze isn't that bad

[SciBomb97]

So regionals was yesterday. We were in optics doing the laser shoot. It turns out that those proctors didn't know how to properly secure the laser to the table or mount mirrors properly. The mirrors has magnets on the back, and were stuck to L-shaped iron thingys. The first time 'round, the laser was going exactly as it should have been, except the third mirror was apparently jacked up and angled slightly down, so the laser his the floor of the box. It was on the line that I traced out on the template exactly as the laser should have been going. If that mirror hadn't been angled down, the laser might have hit with an accuracy of 5 +/- 3 mm. So, we had to redo the whole thing with the mirrors pasted to the other side of the L-shaped iron thingys, and because the bottom of the L-shaped thingys were protruding out in front of the mirror itself, the laser completely missed the fourth mirror and ended up hitting the wrong wall of the box. Also, the block that the laser mounted to was secured to the table with 8 pieces of masking tape (aka, the least adhesive tape there is out there).
We placed 3rd, after two of the teams that we coached...what a failure...

That would be frustrating! My sympathies are with you sir.
But really, bronze isn't that bad

Well, our regionals isn't all that competitive, and there were only 19 teams.
Also, we placed 10th at nats last year, so my expectations were slightly higher. Oh well...

[foreverphysics]

That was bad. Really bad.
They didn't even put in a barrier. SciBomb and I were like, "Whut."
We probably got the highest score overall on the test, because we hit the adjacent wall...and still medaled. The middle school team obviously did really well in the laser shoot, because they came back in and were like, "Yes! Yes!!!" So encouraging... >.<
And then there was that question that was like this:
"A hydrogen atom jumps to its first excited state with an unknown energy. Its second excited state has an energy level of 3.08 x 10^-15. Its third excited state has an energy level of 4.15 x 10^-15. Calculate all three energy levels, wavelengths, and frequencies."
We had no idea what to do with this.

[SciBomb97]

That was bad. Really bad.
They didn't even put in a barrier. SciBomb and I were like, "Whut."
We probably got the highest score overall on the test, because we hit the adjacent wall...and still medaled. The middle school team obviously did really well in the laser shoot, because they came back in and were like, "Yes! Yes!!!" So encouraging... >.<
And then there was that question that was like this:
"A hydrogen atom jumps to its first excited state with an unknown energy. Its second excited state has an energy level of 3.08 x 10^-15. Its third excited state has an energy level of 4.15 x 10^-15. Calculate all three energy levels, wavelengths, and frequencies."
We had no idea what to do with this.

Actually, the 2nd place team also missed the laser shoot completely. I don't know what happened there...

[illusionofconfusion]

Actually, the 2nd place team also missed the laser shoot completely. I don't know what happened there...

But we actually hit all five mirrors, unlike you. That means we got a 20, and y'all got a 12. Therefore, we beated you.

A hydrogen atom jumps to its first excited state with an unknown energy. Its second excited state has an energy level of 3.08 x 10^-15. Its third excited state has an energy level of 4.15 x 10^-15. Calculate all three energy levels, wavelengths, and frequencies.

My partner did a bunch of complicated math... And got an answer.

[foreverphysics]

I think I tried doing a systems of equations until I realized that there would be always one more variable than equation. So then SciBomb did...something with E=hc/l, and I just kinda looked over it and was like, "You missed three parts of it."

[Infinity Flat]

And then there was that question that was like this:
"A hydrogen atom jumps to its first excited state with an unknown energy. Its second excited state has an energy level of 3.08 x 10^-15. Its third excited state has an energy level of 4.15 x 10^-15. Calculate all three energy levels, wavelengths, and frequencies."
We had no idea what to do with this.

This is a wave-particle duality question, which is supposed to be a C topic, but you should probably know anyway.

According to quantum mechanics, all particles (including photons and matter / atoms) also exhibit wave-like properties. This is known as the wave-particle duality. Now, the energy of a particle and the frequency of its wave are related by the simple equation:
E = h v
Where E is the energy of the photon / atom in Joules
h is Planck's constant, 6.626 × 10^−34 J * s
and v (nu) is the frequency of the light in Hertz ( 1/s )
If you know the energy, you can calculate the frequency, and vice versa.

The de Broglie wavelength is a little more complicated, and is given by
wavelength = hc / pc
Where h is Planck's constant, c is the speed of light, and p is the momentum of the particle.
For a photon, pc = E.
For massive particles (electrons), however pc = sqrt{ 2 KE m_0 c^2}
where KE is the kinetic energy, m_0 is the rest mass, and c is again the speed of light.

In an atom, the difference between consecutive energy levels is always the same, so to find the first excited state you would find the difference between the second and the third, and then go from there.

However, this question is quite poorly worded, as its unclear if it's asking about the atom as a whole, the single electron in the atom, or the photon emitted when an electron drops from that excited state to its base state.
Because the Kinetic Energy (or speed) is not given anywhere in the problem, you can't find the wavelength unless its asking about the photon, so you'd have to calculate for the photon.

I'll stop here for now, but I can do the actual calculations for this problem if you're still confused.

[foreverphysics]

It was an electron (I think?). It would be greatly appreciated if you could actually solve the problem.

[SciBomb97]

Wait, isn't the difference in energy between consecutive electron shells different depending on which energy levels they are?

[Infinity Flat]

Wait, isn't the difference in energy between consecutive electron shells different depending on which energy levels they are?

They are, my mistake. I can't remember how exactly they're related off the top of my head, but I believe it involves the Rydberg equation.