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Use the data in Appendix $mathrm{D}$ to find the total kinetic energy released in the $eta^{-}$ decay of ${ }^{14} mathrm{C}$ (See Problem 17.19.)...

Question

Use the data in Appendix $mathrm{D}$ to find the total kinetic energy released in the $eta^{-}$ decay of ${ }^{14} mathrm{C}$ (See Problem 17.19.)

Use the data in Appendix $mathrm{D}$ to find the total kinetic energy released in the $eta^{-}$ decay of ${ }^{14} mathrm{C}$ (See Problem 17.19.)



Answers

The atomic mass of $^1$$^4$C is 14.003242 u. Show that the $\beta$$^-$ decay of $^1$$^4$C is energetically possible, and calculate the energy released in the decay.

Okay, So when the beta minus represent an electron with a negative one as Hama number So therefore the expression here described the beta minus decay off the carbon 14 years case, which is Ah Coburn 14 to trump lusty nitrogen. Since we know the mass number 40 veterans zero, which means that the mass number for the car burn will be remanded saying, which is, you know, 14. But the Tommy number is negative one, which means that a time number off the carbon will be increased one which is evil seven. So I was 7 14 In such elements, it's nitrogen and we know the energy committee Delta, M and C Square. Tell em, was the change in Mass C square is this speed of lice where another change of mass used to go to M C. Minus Emma, since the mass of electrons is negligible in his case, So now okay, implying the value for the time mass for the carbon and the natural in eventually have the Chinese mass is equal to 0.16 a. You and when I see square can be expressed as 931.5 make trouble for you. So now let's plug invented the question to determine the energy that was released, which is equal to zero point 000 16 you times 931 point Fire may go there, John Worlds, are you? And this is people too. 1.56 times tend to the power off. If I Yeah, that's on boats, which is 156 Kyul you got from roads and this is the answer for this question.

Let's write down. Beat a ballistic acreage in beat up lis uh, decay secret gin. Um, well, we have sodium. And they with the atomic mass off 22 atomic number off 11. And this undergoes beat a plastic A and the resulting nucleus. Is he an atomic number or 10? And atomic mass eyes the same. 22 less, uh, beat up less. And then we have new training. Well, energy released in decay. He's, uh uh We need to find out in their energy. Relation to decay. Let's find a Delta am Delta me cools, uh mm into ah, well, Saudi, um, with Tommy command. So 22 minus. Uh, then, uh, Marcelo book this element and e with atomic mess off 22. Um, so most of sodium in Moscow and me. So delta and musical to moss off M A is 21 point mine mine Double four, 34 minus and muscle. And these 21 0.9 mine Ah, one tree If 31383 And this gives this 0.30 51 Hi Atomic mass units. Well, no. Let's find Opener. She Well, we know that e equals M C square here and mist Tel toe him and then c square and we know they'd want atomic mass unity closed mind 31.5 1,000,000 Electron Walt, divided by C Square and therefore inner. She is a cold too. 0.3051 into mine, 31.5 1,000,000 electron volt 1,000,000,000 Electron won't divided by C Square and we multiply this script and therefore energy. It's a cold too. Two point 2.8 for two 1,000,000 electron Oops!

The decay collision for carbon 11. So this is what a decay prison for carbon 11. Ah, here 65 decays you to put on water on 11. Five, uh, six plus better caused You was due. Plus, let's call neutrino in part B were asked to find energy immediate. So I know what you mean to do rescue and by change in mice times the speed of light square. So changing him this vehicle Thio mass off the carbon 11 Troubling the 11 minus amounts off the boat on 11 mining plus two electrons to electron mass. Uh, then substituting the value for the mass off the carbon level on the boat on plus the mass of the electron. Then we have a telling him he's a court to one point 03 times 10 to the power minus three. Um, you times d'oh um three and nine to you. One 0.5 Mega electron, Walt. Maybe like Cornwall's. But you Marcie's where? Dimes C Square, Thomas C Square. These courses were cancel utensils and multiplying those two numbers. Here's a zero point 96 02 Mega Electron wants. So the energy emitted Is this amount. End off the problem. Thank you for watching

In number 30. I'm defined the energy released in Alfa Decay of uranium to 38. So I'm gonna write my equation first. I start with uranium to 38 and they told me it's off. Okay, so I know that my one daughter will be an alpha particle and the other one just have a mass number off for less than a B 2 34 And it has to have two less protons. That's 90. And yes, that is Thor him. And they told me that. So now I'm just going to consider the masses back in the back. In appendix B, I looked at the mass for uranium to 38. It is 2 38 point 050 783 use, um, thorium. They told me here. They told me it was 2 34 0.43 and an Alfa particle. It's 4.2602 And these are all use atomic mess units. So I want to find the energy I find how much mass missing here. So basically have it right here. If I want to find the missing mass, it's going to be this minus these And when I do that, I get 0.5 one each one. You gonna convert that to the energy equivalent? I know that one. You is the same as 931 point 494 mega electron volts. So you canceled. And my energy is 4.82 mega electron volts.


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