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Energy Levels

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Question 1 0:25
  • Question 2 1:18
  • Question 3 1:43
  • Question 4 2:08
  • Question 5 3:17
  • Question 6 3:54
  • Question 7 4:40
  • Question 8 5:15
  • Question 9 5:54
  • Question 10 6:41
  • Question 11 7:14

Transcription: Energy Levels

Hi everyone and welcome back to 0000

I am Dan Fullerton and today we are going to go through page 1 of the APlusPhysics worksheet on energy levels. 0003

And as you do these, it is probably going to be helpful to have a diagram of the energy levels -- energy level diagrams for both hydrogen and for mercury. 0009

You can find a copy of this worksheet on the APlusPhysics site at the video link down below. 0018

Number 1 -- An electron and a mercury atom drops from an energy level (I) to the ground state by emitting a single photon. 0025

This photon has an energy of -- well to do this-- the energy of our photon is going to be the energy of our initial level minus our final energy level. 0033

I look up on my energy level diagram for mercury and find that the energy level for (I) is going to be about -1.56 eV and that is minus the ground state, which is going to be -10.38 eV. 0044

Therefore the energy of that photon -1.56 + 10.38 = 8.82 eV -- Answer number 2. 0063

Number 2 -- White light passes through a cloud of cool hydrogen gas and is examined with a spectroscope. 0078

The dark lines observed on a bright background are caused by -- well that is going to be caused by the absorption of the specific frequencies that allow electrons to jump to higher levels. 0083

So that is going to be correct answer Number 2 -- The hydrogen absorbing certain frequencies of the white light. 0094

Number 3 -- The bright line emission spectrum of an element can best be explained by -- well that is going to be caused by electrons falling down from higher states to lower states and emitting a photon of a specific frequency relating to the energy between those energy level transitions. 0103

The correct answer here is going to be 1 -- Electrons transitioning between discreet energy levels in the atoms of that element. 0119

Number 4 -- Explain why a hydrogen atom in the ground state can absorb a 10.2 eV photon, but cannot absorb an 11 eV photon. 0129

Well, the key here is atoms can only absorb photons with energies that are exactly equal to the amount that will allow an electron to jump to a higher energy state. 0138

So 10.2 eV must be the difference between two energy levels that are allowed, where 11 electron volts does not bring you from one energy level completely to another energy level. 0148

I would write something like, 'You can only absorb photons...0161

...with energy exactly equal to the difference in allowed energy levels.' 0169

Let us move on to Number 5 -- Excited hydrogen atoms are all in the N = 3 state. 0194

How many different photon energies could be emitted as these atoms return to the ground state? 0201

If we have the 3rd level, 2nd level and the N = 1 level, an electron could fall from 3 to 2, so there is one possible photon energy. 0206

It could fall from 2 to 1, so there is another possible photon energy, and it could fall all the way from 3 to 1 in one shot, so I would say we have three different possible photon energies, so the correct answer there is Number 3. 0218

Number 6 -- How much energy is required to move an electron in a mercury atom from the ground state to energy level (H)?0234

We are going to need the energy level diagram for mercury to do this one and to do that remember the energy of a photon is its initial minus its final energy levels. 0240

So that is going to be -1.57 - -10.38 = 8.81 eV. 0252

I did those backwards, because we are starting at the ground state going up and it is absorbing that photon in order to move to energy level (H) -- 8.81 eV -- Answer Number 2. 0267

Number 7 -- An electron and a hydrogen atom drops from the N = 3 energy level to the N = 2 energy level. 0280

What is the energy in electron volts of the emitted photon? 0286

We are going to need the hydrogen energy level diagram here. 0289

The energy of our photon is the initial minus the final energy level, which is -1.51 eV at the N = 3 and it is -3.4 eV at the N = 2, so that is going to give us 1.89 eV. 0292

Number 8 says what is the energy in joules of that emitted photon? 0316

So we are going to take 1.89 eV and we need to convert that into joules, so if I want electron volts to go away, I put that in the denominator and if I want joules, I put that in the numerator and I know 1 electron volt is 1.6 × 10-19 J. 0319

My electron volts will make a ratio of 1, therefore I am going to be left with 1.89 × 1.6 × 10-19 units J, which will give us 3.02 × 10-19 J. 0336

Number 9 -- An electron in the hydrogen atom drops from N = 3 to 2. Calculate the frequency of this emitted radiation now. 0354

Well, the energy is (HF), therefore our frequency is going to be E/H. 0363

We just determined our energy was 3.02 × 10-19 J and we have for our (H), Planck's constant, 6.63 × 10-34 J/s.0371

When I run through that with my calculator, I come up with a frequency of 4.56 × 1014 Hz. 0385

Two more -- Calculate the wavelength of the emitted radiation. 0401

Well, velocity is frequency times wavelength, which implies that wavelength equals velocity over frequency. 0405

Our velocity is 3 × 108 m/s/4.56 × 1014 Hz (frequency) gives us a wavelength of about 6.58 × 10-7 m or 658 Nanometers. 0412

Last problem here -- A hydrogen atom with an electron initially in the N = 2 level is excited until it is in the N = 4 level. 0434

This energy level change occurs because the atom -- well to go from a lower to higher energy level, first off, it must absorb a photon, so we could get rid of any of the emitted answers. 0441

To find the energy of that photon, the energy of our photon is going to be its initial level minus the final level or -3.4 eV from N = 2 level to -0.85 eV from the N = 4 level or -2.55 eV...0452

...where that negative just means that it is absorbing that photon, so the correct answer must be Number 3. 0471

That concludes the first page of this worksheet.0479

If all of that went great -- Terrific -- Go ahead and move on or if it did not go so well, now would be a great time to go back and review that section of our lecture. 0482

Thanks for your time and make it a great day everyone. 0490