Calculating Energy from Mass Using E=mc²

[ElegantSir]

Homework Statement

I have the question with a diagram posted in the thumbnail to make things easier.

Homework Equations

E = mc²

The Attempt at a Solution

The homework only had a single example for a question like this so I am not 100% sure how to get the answer. So far I've added the 2 masses:
5.030151g and 5.011267g

Then I subtracted them both 5.030151 – 5.011267 = 0.018884g

Here is where I am stuck. I know that from the example I need to do something like 1.8884 * 10^(input some number here) but I have no clue how to get the number that it should be to the power to. All I know is after this I need to multiply 1.8884 * 10 ^ (?) by 3.8 * 10 ^ 8 to calculate the total amount of energy produced using E = mc²

 

[SteamKing]

Homework Statement

I have the question with a diagram posted in the thumbnail to make things easier.

Homework Equations

E = mc²

The Attempt at a Solution

The homework only had a single example for a question like this so I am not 100% sure how to get the answer. So far I've added the 2 masses:
5.030151g and 5.011267g

Then I subtracted them both 5.030151 – 5.011267 = 0.018884g

Here is where I am stuck. I know that from the example I need to do something like 1.8884 * 10^(input some number here) but I have no clue how to get the number that it should be to the power to. All I know is after this I need to multiply 1.8884 * 10 ^ (?) by 3.8 * 10 ^ 8 to calculate the total amount of energy produced using E = mc²

Why are you assuming that the masses of the elements reacting are not in grams?

I think you are assuming, based on the wording of the question, that only 1 atom of D and T react, but that need not be the case. Only the ratios of the reactants matter.

Also, units should be carefully scrutinized here. If you take c in m/s, what mass units must you use in order to calculate energy in joules?

 

[ElegantSir]

Why are you assuming that the masses of the elements reacting are not in grams?

I think you are assuming, based on the wording of the question, that only 1 atom of D and T react, but that need not be the case. Only the ratios of the reactants matter.

Also, units should be carefully scrutinized here. If you take c in m/s, what mass units must you use in order to calculate energy in joules?

Im not quite sure what you mean by all of that. I assume you mean I need to convert grams to a different unit of measurement but I am not sure what. Also what do you mean by
"I think you are assuming, based on the wording of the question, that only 1 atom of D and T react?"

 

[SteamKing]

Im not quite sure what you mean by all of that. I assume you mean I need to convert grams to a different unit of measurement but I am not sure what.

Well, joules are the SI units of energy. Joules are also derived units. What is the definition of a joule?

https://en.wikipedia.org/wiki/Joule

Also what do you mean by
"I think you are assuming, based on the wording of the question, that only 1 atom of D and T react?"

It's obvious that 1 atom of deuterium does not have a mass of 2.014102 g, but a certain number of deuterium atoms does have this total mass. Ever heard of a fellow by the name of Avogadro?

https://en.wikipedia.org/wiki/Avogadro_constant

If you're going to study physics, you've got to study units and understand how units are useful in deciphering physics problems.

 

[ElegantSir]

Well, joules are the SI units of energy. Joules are also derived units. What is the definition of a joule?

https://en.wikipedia.org/wiki/Joule
It's obvious that 1 atom of deuterium does not have a mass of 2.014102 g, but a certain number of deuterium atoms does have this total mass. Ever heard of a fellow by the name of Avogadro?

https://en.wikipedia.org/wiki/Avogadro_constant

If you're going to study physics, you've got to study units and understand how units are useful in deciphering physics problems.

Ahh I see where I went wrong. The example

 

[ElegantSir]

Ahh I see where I went wrong. The example questions like to use numbers like 1.9 * 10^-4 rather than use the actual whole number so I got confused.

I would need to convert grams to kilograms which would mean the number would now become: 1.8884 * 10^-5
Now I plug it into E = mc^2 and get:

E = 1.8884 * 10^-5 * (3 * 10^8)^2
E = 1.7 * 10 ^ 12 (rounded of course)

Im assuming this is the correct answer now?

 

[SteamKing]

Ahh I see where I went wrong. The example questions like to use numbers like 1.9 * 10^-4 rather than use the actual whole number so I got confused.

I would need to convert grams to kilograms which would mean the number would now become: 1.8884 * 10^-5
Now I plug it into E = mc^2 and get:

E = 1.8884 * 10^-5 * (3 * 10^8)^2
E = 1.7 * 10 ^ 12 (rounded of course)

Im assuming this is the correct answer now?

Always include the units in your calculation results. That's a habit you should acquire now.

 

[ElegantSir]

Always include the units in your calculation results. That's a habit you should acquire now.

Ahh yes it would be in Joules...Thanks for the help!