Question

2. The data in the table show the amount of a 500 g sample of sodium-24 over time.
Make a graph of the data, labeling all axes and adding a title.
What is the half-life of sodium-24? Explain your answer.
Sodium-24 decays by beta emission. Write a nuclear equation that shows the decay of sodium-24 and
its products.

Answer 1

Is the half-life 250? or is it 8? I'm thinking 250 but the half-life could mean the half of the half of the half life, right?

Answer 2

here someone else asked this question see if it'll help you out.

Answer 3

@Fandude727 Was there supposed to be a link or something?

Answer 4

How much do you have at the start?

Answer 5

500 g

Answer 6

Oh sorry. http://openstudy.com/study#/updates/53702d17e4b0d61a13c860d9

Answer 7

What is 1/2 of 500?
At what time do you have that amount left?

Answer 8

250 g and the time would be 15 h

Answer 9

Right. So the half-life is 15 hours. If you take any point in the table, observe the amount Na at that point, then go look at the entry 15 hours later, it should be 1/2 of the amount of Na at the earlier spot.

Answer 10

Oh okay, I got it can you help me with the equation part?

Answer 11

After 1 half-life elapses, 1/2 of the original material has undergone decay.

Of course!

Answer 12

What is the atomic number of Na? And the atomic mass?

Answer 13

The atomic number of Na is 11 and the mass is 22.99 g/mol

Answer 14

If we lose a beta particle from the nucleus, what happens? What change and mass does the beta have?

Answer 15

We have one extra proton and electron?

Answer 16

Beta emission is effectively the splitting of a neutron into a proton (which stays) and the beta particle (which leaves). So we start with 11 protons and 23-11 = 12 neutrons in the nucleus. We split one of those neutrons into another proton and a beta particle, which we emit, leaving us with 11+1 = 12 protons, and 12-1=11 neutrons. What element is that?

Answer 17

Magnesium?

Answer 18

@whpalmer4 ?

Answer 19

Yes, magnesium is correct.

For something cool, have a look at this: http://www.periodictable.com/Isotopes/011.24/index.dm.html
which shows the decay mode. Explore some of the other isotopes and see how they decay.

Answer 20

So your decay equation looks like

\[{\text{Na}_{11}}^{24}\rightarrow {e_0}^1 + {\text{Mg}_{12}}^{23}\]

Answer 21

I said earlier that we had 12 neutrons and 11 protons, but that was for Na-23 and we are using Na-24 here, so there is 1 more neutron: 13 neutrons and 11 protons. As most sodium atoms are Na-23 and some are even lighter isotopes, the average atomic mass is about 23, but for Na-24 alone it is about 23.99 atomic mass units.

Answer 22

@whpalmer4 Danke! You're a better teacher than mine :D

Answer 23

Better version:
\[~_{11}^{24}\text{Na}\rightarrow ~_{-1}^{0}e + ~_{12}^{24}\text{Mg}\]

You can see if you add across at the same position, we always have the same sum on each side of the arrow.

24 = 0 + 24
11 = -1 + 12

Answer 24

My previous answer was incorrect. Too long since my last caffeine infusion :-)

Answer 25

Haha "caffeine, the only way to keep us on track"

Answer 26

it's not just for breakfast any more!

Answer 27

It never was!

Answer 28

Were you able to make a nice graph from the table?

Answer 29

Ja, I was able to make a decent graph thanks to you!