# Chemistry

posted by .

The half life of U238 is 4.5 x 10^9 yr. A sample of rock of 1.6 g produces 29 dis/sec. Assuming all radioactivity is due to U238 find percent by mass of U 238.

I have tried
ln(t)/ln(0)= -kt and still cannot get the answer
What I get is
A) 4.5x10^9 x365x60x60x24=1.419x10^17 for half life
B) .693/1.419x10^17=4.883x10-18

C) ln t/ln 29= -(4.883x10^-18)

That is the farthest I've gotten. Can someone help?

• Chemistry -

Use Nt/N0 = e^{-kt}
1[yr] = a = 31557600[s]

(1/2) = e^(-kh)
Where:
Half life: h= 4.5e9 * a = 1.420092E+17[s]

k = -ln(0.5)/1.420092E+17
.: k = 4.8810019E-18[/s]

Okay, so far. To continue...
Assume there is n atoms of U238 in the sample. t=1 second latter there is n-29. (via 29 disintegrations per second)

(n-29)/n = e^{-kt}
1 - (29/n) = e^{-kt}
29/n = 1-e^{-kt}
n = 29/(1-e^{-kt})
n = 29/(1-exp(-4.8810019E-18))
n = 5.9414031E+18[atoms]

Next: find the weight of this number.
Given:
1[mole]=6.02214129(27)E+23[atoms]
U[238] weighs 238.05078822[g/mol]

Express as a percentage of the sample weight (1.6[g]).

## Similar Questions

A Cesium 137 sample has a measured radioactivity of 50 microcuries.Cesium 137 has a half-life of 30 years. How long will it take this sample to be reduced to a residual radioactivity of 6.25 microcuries?
2. ### Chemistry *URGENT*

URGENT help! 3. A rock sample was dated using potassium-40, Neasyrenebt ubducated tgat 1/8 of the original parent isotope is left in the rock sample. How old is the rock?
3. ### Half-Life

Uranium-238 decays to Lead-206. The half life of Uranium-238 is 4.5 billion years. If you have a 100 g sample. How much sample will you have after 2 half lifes?
4. ### chemistry

I have: the half life of U-238 is 4.5 x 10^9 yr. A sample of rock of mass 1.6g produces 29 disintegrations per second. find percent by mass of U-238 in rock. I have 4.5x 10^9x60x60x365x24=1.419x 10^17= .693/1.419 x10^17 =4.883x10^-18 …
5. ### Chemistry

I don't know if I should be posting this on a new session or just the old one; I asked it yesterday and I have not seen a reply I have: the half life of U-238 is 4.5 x 10^9 yr. A sample of rock of mass 1.6g produces 29 disintegrations …
6. ### Chemistry 1046

Geologists can estimate the age of rocks by their uranium-238 content. The uranium is incorporated in the rock as it hardens and then decays with first-order kinetics and a half-life of 4.5 billion years. A rock contains 65.7% of the …
7. ### Chemistry

Geologists can estimate the age of rocks by their uranium-238 content. The uranium is incorporated in the rock as it hardens and then decays with first-order kinetics and a half-life of 4.5 billion years. A rock is found to contain …
8. ### Chemistry

Pu-238 is radioactive by alpha-decay (half-life 87.7 y). Each decay releases 5.6 MeV of energy. Pu-238 is sometimes used to power space probes. If all the decay energy can be converted to electric power, what mass of Pu-238 would be …
9. ### Chemistry (Dr.Bob222)

The half-life of P-32 is 14 days. How long after a sample is delivered can a laboratory wait to use a sample in an experiment if they need at least 10 percent of the original radioactivity?
10. ### college gen chem

An igneous rock contains a Pb−206/U−238 mass ratio of 0.367. How old is the rock?

More Similar Questions