How Many Sodium Atoms Remain in the 3p State After 10ns?

[fredrick08]

Homework Statement

1x10^6 sodium atoms are excited to the 3p state at t=0s. The lifetime of the 3p state is 17ns.

a.how many of these atoms remain in the 3p state at t=10ns?
b.how many photons have been emitted from t=0s to t=30ns?

Homework Equations

N=Noe^(-t/$$\tau$$)

The Attempt at a Solution

a. N=1x10^6*e^(-10ns/17ns)=5.55x10^5 sodium atoms
b. N=1x10^6*e^(-30ns/17ns)=171237 sodium atoms
thus N-No=828763 sodium atoms undergo quantum jump during the first 30ns, each of these atoms emits a photon, thus 828763 photons are emitted.

Im not sure if these are correct, but can't find where I've gone wrong, is it ok to do it like that and that the fact that the 17ns lifetime... doesn't have any effect on the 30ns... please can someone confirm that I am right or help me where i have gone wrong thanks.

 

[LowlyPion]

Homework Statement

1x10^6 sodium atoms are excited to the 3p state at t=0s. The lifetime of the 3p state is 17ns.

a.how many of these atoms remain in the 3p state at t=10ns?
b.how many photons have been emitted from t=0s to t=30ns?

Homework Equations

N=Noe^(-t/$$\tau$$)

The Attempt at a Solution

a. N=1x10^6*e^(-10ns/17ns)=5.55x10^5 sodium atoms
b. N=1x10^6*e^(-30ns/17ns)=171237 sodium atoms
thus N-No=828763 sodium atoms undergo quantum jump during the first 30ns, each of these atoms emits a photon, thus 828763 photons are emitted.

Im not sure if these are correct, but can't find where I've gone wrong, is it ok to do it like that and that the fact that the 17ns lifetime... doesn't have any effect on the 30ns... please can someone confirm that I am right or help me where i have gone wrong thanks.

The lifetime here I believe is the mean lifetime. Results in nature may vary over a set of 10⁶.

The equations you've set up look ok to me. Assuming only 1 photon is available in the 3p of each to go to the 3s, then your answer would seem to be good.

 

[borgwal]

Yes, there is only one photon "available" to go from 3p to 3s. More precisely, the Na atom could also decay by emitting 3 photons (each with roughly a third of the energy difference between 3p and 3s), but that process is much much much less likely.

I would deduct points though for using way too many digits in your answer.

 

[fredrick08]

ok then thanks very much for ur help