Calculate the difference between initial and the final masses

[amazingphysics2255]

Homework Statement

Polonium-212 decays into Lead-208, emitting an alpha particle. The mass of polonium is $$3.51986x10^-25kg$$ The mass of lead is $$3.45323x10^-25kg$$ and the mass of an alpha particle is $$6.646x10^-27kg$$

Calculate the difference between the initial and final masses of the reaction

Relevant Equations

None given

Don't really know how to go about this exercise as I've been given no information for it I tried googling similar problems but couldn't find any
If someone could give me a process to try I will then try to solve it here in this section, thanks.

 

[RPinPA]

This seems very simple. Maybe I'm missing something. You want to know the difference between initial and final mass.
You're told what you have initially (Po-212).
You're told its mass.
You're told what you have finally (Pb-208 + alpha).
You're told their mass.

That's the initial mass and the final mass. So what else do you need to know to find the difference between those two masses?

 

[amazingphysics2255]

This seems very simple. Maybe I'm missing something. You want to know the difference between initial and final mass.
You're told what you have initially (Po-212).
You're told its mass.
You're told what you have finally (Pb-208 + alpha).
You're told their mass.

That's the initial mass and the final mass. So what else do you need to know to find the difference between those two masses?

Do I need to subtract one from another?

 

[RPinPA]

Yes, that's what "difference" means.

 

[amazingphysics2255]

Yes, that's what "difference" means.

So I'm meant to take 3.51986x10−25kg off 3.45323x10−25kg ? giving me 0.06663? why am I given the alpha particles mass? am I supposed to use it?

or was I mean to add 3.45323+6.646 together then take 10.09923-3.51986=6.57937

 

[collinsmark]

So I'm meant to take 3.51986x10−25kg off 3.45323x10−25kg ? giving me 0.06663? why am I given the alpha particles mass? am I supposed to use it?

or was I mean to add 3.45323+6.646 together then take 10.09923-3.51986=6.57937

It might make more sense if you write out the nuclear reaction equation first. Keep in mind the alpha particle is the same thing as a helium nucleus, ^4_2\rm{He}.

So the reactants and products involve ^{212}_{\ 84}\rm{Po}, \ ^{208}_{\ 82}\rm{Pb} and ^4_2\rm{He}

Which are the reactants and which are the products?

 

[amazingphysics2255]

Well
$$ ^{212}_{\ 84}\rm{Po}, \ ^{208}_{\ 82}\rm{Pb}, ^4_2\rm{He}$$

Po must be a reactant and Pb is a product

$$ ^{212}_{\ 84}\rm{Po}\rightarrow \ ^{208}_{\ 82}\rm{Pb}+ ^4_2\rm{He}$$
Is that the reaction written down?

 

[collinsmark]

$$ ^{212}_{\ 84}\rm{Po}\rightarrow \ ^{208}_{\ 82}\rm{Pb}+ ^4_2\rm{He}$$
Is that the reaction written down?

Correct! So now just add up the masses on each side and find the difference. That's the mass deficit.

If the mass of the products is less than the mass of the reactants, it means a net amount of energy was released (as opposed to absorbed) during the reaction.

 

[amazingphysics2255]

Correct! So now just add up the masses on each side and find the difference. That's the mass deficit.

If the mass of the products is less than the mass of the reactants, it means a net amount of energy was released (as opposed to absorbed) during the reaction.

So 3.51986x10^−25kg-3.45323x10^−25kg= 0.06663x10^-25. Was I meant to add the alpha particles mass onto the lead than deduct?

 

[collinsmark]

So 3.51986x10^−25kg-3.45323x10^−25kg= 0.06663x10^-25. Was I meant to add the alpha particles mass onto the lead than deduct?

Do that calculation over. You are correct that you first need to add the mass of the alpha particle to the mass of the lead nucleus first.

The mass deficit is the difference in mass between the total mass of all the reactants and the total mass of all the products.

Assuming the reaction releases a net amount of energy (instead of absorbing energy), the total mass of the products will be less than the total mass of the reactants and the mass deficit will be positive.*

*[Edit: This is also assuming that none of the particles are moving at relativistic speeds. Particles moving at relativistic speeds will be important soon when you study beta decays. But don't worry about that for this problem.]

 

[amazingphysics2255]

Do that calculation over. You are correct that you first need to add the mass of the alpha particle to the mass of the lead nucleus first.

The mass deficit is the difference in mass between the total mass of all the reactants and the total mass of all the products.

Assuming the reaction releases a net amount of energy (instead of absorbing energy), the total mass of the products will be less than the total mass of the reactants and the mass deficit will be positive.

3.45323x10−25kg+6.646x10−27kg=10.09923^-27kg

3.51986x10−25kg-10.09923^-27kg=6.657937^-27kg

I have a feeling this is still wrong as the Polonium-212 is emitting an alpha particle so should the alpha particle also be added to the Polonium-212 then that amount is taken off the 10.09923?

 

[collinsmark]

3.45323x10−25kg+6.646x10−27kg=10.09923^-27kg

Try that calculation again. Keep in mind that 6.646 \times 10^{-27} \ \rm{kg} = 0.06646 \times 10^{-25} \ \rm{kg}

I have a feeling this is still wrong as the Polonium-212 is emitting an alpha particle so should the alpha particle also be added to the Polonium-212 then that amount is taken off the 10.09923?

There's no need to add the mass of the alpha particle to the mass of the polonium nucleus.

In a sense, the alpha particle is already "inside" the polonium nucleus to begin with. It's already in there. No need to add it again. The mass of polonium nucleus already "contains" (so to speak) the mass of the alpha particle.

 

[amazingphysics2255]

3.45323x10^−25kg+0.06646×10^−25 kg=3.51969x10^-25kg

3.51986x10−25kg-3.151969x10^-25kg=0.367891x10^-25kg

Please be right, haha

 

[collinsmark]

3.45323x10^−25kg+0.06646×10^−25 kg=3.51969x10^-25kg

3.51986x10−25kg-3.151969x10^-25kg=0.367891x10^-25kg

Please be right, haha

The first calculation looks correct.

But I think you misstyped an extra "1" digit into one of your numbers that doesn't belong. I've highlighted the digit in red.

 

[amazingphysics2255]

yeah, I did good catch, so it supposedly is 0.00017x10^-25kg

 

[collinsmark]

yeah, I did good catch, so it supposedly is 0.00017x10^-25kg

That looks correct to me.

 

[amazingphysics2255]

$$E=mc^2$$ so
$$E=0.00017x10^-25(3.00x10^8)^2$$

which = 15278838mj

is this also correct?

 

[collinsmark]

$$E=mc^2$$ so
$$E=0.00017x10^-25(3.00x10^8)^2$$

which = 15278838mj

is this also correct?

I think it might be off by a factor of 10, according to my calculations.

[Edit: On the other hand, if you are using units of milli-Joules, then you are off by many orders of magnitude.]

 

[amazingphysics2255]

So what would I need to do to fix this?

 

[collinsmark]

So what would I need to do to fix this?

just try redoing the calculation. Maybe you missed or added a digit or something.

[Edit: Now that I notice your units, your answer seems to be off by many orders of magnitude. Maybe something went wrong with your exponents.]

 

[amazingphysics2255]

ok I've redone it now getting $$1.53x10^-12kg$$ also what's a good way to convert this to joules, mega joules?

 

[collinsmark]

ok I've redone it now getting $$1.53x10^-12kg$$ also what's a good way to convert this to joules, mega joules?

The numerical value is correct, but it should have units of Joules. 1.53 \times 10^{-12} \rm{J}
(not kg.)

If you want to get rid of the 10^{-12} the prefix for that is pico-.

 

[amazingphysics2255]

Ok, so Let's me practice one last one M(mass)=0.0024845×10^−26kg $$E=mc^2$$ $$E=0.0024845×10^−26kg(3.00x10^8)^2$$ $$=2.23605x10^-12J$$

 

[collinsmark]

Ok, so Let's me practice one last one M(mass)=0.0024845×10^−26kg $$E=mc^2$$ $$E=0.0024845×10^−26kg(3.00x10^8)^2$$ $$=2.23605x10^-12J$$

Assuming that one is just for practice (I don't know how that mass applies to this problem specifically), then yes, the calculation looks correct to me.

 

[amazingphysics2255]

Assuming that one is just for practice (I don't know how that mass applies to this problem specifically), then yes, the calculation looks correct to me.

Yeah that mass has nothing to do with this problem, just making sure I'm proficient