# Homework Help: Half life of Uranium question

1. Oct 16, 2011

### paperdoll

1. The problem statement, all variables and given/known data
I'm not sure if whether mass changes when atoms decay. Does emitting alpha/beta/gamma cause the atoms to lose mass? I don't know

2. Relevant equations
Uranium-235 has a half life of 7.35x10^5 years and uranium 238 has a half life of 4.5x10^6 years. Compare the two isotopes of uranium, given that they both have the same number of atoms.

a) Which sample would have the greater weight?
b) which sample would have the greater number of decays per second?

3. The attempt at a solution

For a) I'm not really sure but I think it would be the U-238 because it has the greater half life

For b) I'm not sure if this is right, if shorter half-life means greater decays per second. But I think it should be the U-235

2. Oct 16, 2011

### I like Serena

Hi paperdoll!

Do you know what the number 238 represents?

What is the definition of half-life?

3. Oct 16, 2011

### paperdoll

Hi I like Serena, long time no see ^^ since I haven't posted here for a while :)

Yes, the number 238 represents the amount of protons and neutrons in the Uranium atom

okay, half life is the time it takes for an amount of a substance to decay down to half its original value.

4. Oct 16, 2011

### I like Serena

Yep. I know!
Good that you remember me! :shy:

Yes.
So which atom is heavier?

Right.
So suppose each sample has 2N atoms.
Then N atoms decay from 2N atoms in the corresponding half-time T.
How many decays is that per second?

5. Oct 16, 2011

### paperdoll

Yes, I have my final physics exams soon so I'm going through the past exam papers now :) that means more questions ahah
Oh! So the U-238 must be heavier since it has more neutrons
I'm not really sure about the decays per second. Does the decay per second stay constant throughout the entire decay process or does it slowly get smaller?

6. Oct 16, 2011

### I like Serena

Yep!

That's what I'm trying to get you to find out. :uhh:

If we start with 2N atoms, then after a half-time T, N atoms have decayed.
Can't you calculate the number of decays per second from that?

7. Oct 16, 2011

### paperdoll

would that be N/t decays per second then? o__O
that is, provided that the "t" value is measured in seconds I think :uhh:

8. Oct 16, 2011

### I like Serena

Yep. :)
Note that if t is not in seconds, you can simply convert it to seconds.

Now to answer your last question first - does it decrease in time or not?

9. Oct 16, 2011

### paperdoll

um...so the number of decays per second should decrease after time right? because nuclear decay is an exponential curve, so eventually there will be zero decays per second I think

10. Oct 16, 2011

### I like Serena

Right! ;)

Let's put it this way.

If you start with 2N atoms, you've got N/T decays per second.

After a time T you'd be left with N atoms.
In the next period T, N/2 atoms would decay.
So you have (N/2)/T decays per second.
That's less, isn't it?

It is indeed a downward exponential curve.

Okay.
So if we look at the two samples, of each 2N atoms with half-times T1 and T2.
What are their respective decays per second?
And which is the greater?

11. Oct 16, 2011

### paperdoll

okay hmm, so if I let T1 be U-235= that means 7.35x10^5 years
and let T2 be U-238 = that means 4.5x10^6 years

so the rate of decay will be N/T(1 or 2)

so it is N/(7.35x10^5) and N/(4.5x10^6 years)

so the one with the greater number of decays per second will be N/(7.35x10^5) which is T1 which is U-235

I think I get it now Thank you I like Serena ^^ you made things extremely clear now

12. Oct 16, 2011

### I like Serena

You're welcome!