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 1 answerLast reply by: Professor Dan FullertonTue Dec 23, 2014 6:52 AMPost by Jamal Tischler on December 22, 2014I watch every video in this course. I learned more things about physics. Thank you for your help ! 1 answerLast reply by: Professor Dan FullertonSat Apr 19, 2014 8:30 PMPost by Taylor Wright on April 19, 2014Thank you for this amazing lecture series over AP Physics B!!!  Do you know if there are any plans to incorporate any Engineering specific lectures in the near future such as statics, dynamics, fluids, etc.?Thank you!

### Mass-Energy Equivalence

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 0:19
• Question 2 1:02
• Question 3 1:37
• Question 4 2:17
• Question 5 2:55
• Question 6 3:32
• Question 7 4:13
• Question 8 5:04
• Question 9 5:29
• Question 10 5:58
• Question 11 6:48
• Question 12 7:39

### Transcription: Mass-Energy Equivalence

Hi everyone and welcome back to Educator.com.0000

I am Dan Fullerton and in this mini-lesson we are going to go through Page 1 of the APlusPhysics worksheet on mass energy equivalents and you can find that worksheet by clicking on the link down below the video.0003

Take a few minutes and see if you can work through that and then we will check the answers together.0014

All right. Moving on to Number 1.0019

If a deuterium nucleus has a mass of 1.53 × 10-3 universal mass units less than its components, this mass represents an energy of?0021

Well it must have become an energy, so that is going to be 1.53 × 10-3 universal mass units and we want to convert that into mega-electron volts (MeV).0031

I know that 1 atomic mass unit, universal mass unit is 931 MeV, so our units will cancel out there and I will come up with about 1.42 MeV -- Answer Number 2.0043

Number 2 here -- the energy equivalent of 5 × 10-3 kg is -- well to find the energy equivalent, E = mc2 -- probably heard that one before.0062

That is going to be 5 × 10-3 kg × c (the speed of light in a vacuum), 3 × 108 m/s2.0073

Put all that into my calculator and I come up with an answer of right around 4.5 × 1014 J -- Answer Number 3.0084

On to Number 3 -- How much energy in mega-electron volts is produced when one-quarter of a universal mass unit of matter is completely converted into energy?0097

Well, we have 0.25 universal mass units and we want to convert that into energy in MeV.0107

I know that one universal mass unit gives you 931 MeV, so I can treat this as a unit conversion problem, so 0.25 × 931 = 233 MeV.0115

Number 4 -- The energy equivalent of the rest mass of an electron is approximately -- well again, E = mc2, where our mass, the mass of an electron is 9.11 × 10-31 kg × c (the speed of light), 3 × 108 m/s2...0137

...which implies then that the energy equivalent is going to be -- when I put all of that into my calculator -- about 8.2 × 10-14 J -- Answer Number 2.0156

Number 5 -- The energy produced by the complete conversion of 2 × 10-5 kg of mass into energy is...0174

Well E = mc2 again, where our mass is 2 × 10-5 kg, c (speed of light) 3 × 108 m/s2 is going to give us an energy of right around 1.8 × 1012 J, which is 1.8 tera-joules (TJ) -- Answer Number 1.0183

Number 6 -- What is the minimum total energy released when an electron and its anti-particle, known as a positron, annihilate each other.0213

Well, energy is mc2 again, where our mass is going to be 2 times the mass of an electron because the anti-particle has the same mass, but an opposite charge.0220

That will be 2 × 9.11 × 10-31 kg and our mass times the speed of light in our vacuum, 3 × 108 m/s2, which comes out to be about 1.64 × 10-13 J -- Answer Number 1.0229

Number 7 -- The energy required to separate the 3 protons and 4 neutrons in the nucleus of a lithium atom is 39.3 MeV.0252

Determine the mass equivalent of this energy in universal mass units.0262

We have 39.3 MeV and we want to find out its mass equivalent.0267

Well we want MeV to go away and we want universal mass units and I know that 1 universal mass unit is equal to 931 MeV, so we are multiplying by 1 again.0275

Our units make a ratio of 1 and I come up with, when I do this, 39.3/931 is right around 0.0422 universal mass units.0287

Number 8 -- Which graph best represents the relationship between energy and mass when matter is converted into energy?0304

Well, if E = mc2 and our variables are (E) and (M) -- well C2 is just a constant, so it looks like we have a linear relationship between mass and energy.0311

That is going to be that direct relationship, Number 1.0323

Number 9 -- The total conversion of 1 kg of the sun's mass into energy yields what?0329

Well, let us use E = mc2, where our mass is 1 kg, c (speed of light in a vacuum) 3 × 108 m/s2 is just going to be 9 × 1016 J -- Answer Number 4.0336

That is a lot of energy for 1 kg of mass.0353

Number 10 -- What total mass must be converted into energy to produce a gamma photon with an energy of 1.03 × 10-13 J?0358

Well, before trying to get that energy, we know E = mc2 and we want the mass.0367

Therefore mass is going to be equal to the energy divided by the speed of light squared or 1.03 × 10-13/3 × 108 m/s2 (speed of light in a vacuum)...0374

...which gives us a mass equal to about 1.14 × 10-30 kg -- Answer choice, Number 1.0391

Two more here -- A tritium nucleus is formed by combining two neutrons and a proton.0406

The mass of this nucleus is 9.106 × 10-3 universal mass unit less than the combined mass of the particles from which it is formed.0412

Approximately how much energy is released when this nucleus is formed?0421

Well, to do this, let us convert 9.106 × 10-3 universal mass units into MeV, where I know that 1 universal mass unit is 931 MeV.0425

Universal mass units are going to make a ratio of 1 and I am going to end up with an answer of about 8.48 MeV -- Answer Number 3.0443

Last one on this page -- After a uranium nucleus emits an alpha particle, the total mass of the new nucleus in the alpha particle is less than the mass of the original uranium nucleus.0458

Explain what happens to the missing mass.0469

Well, that missing mass must have been converted into energy.0472

All right, if you struggled with this it would be a great time to go back and review the sections on nuclear physics.0482

If this went well -- Terrific -- Now you are probably ready to go tackle some of the AP level problems.0487

Thanks so much for your time everyone and make it a great day.0492