Is the uranium in equilibrium with its progeny, in particular, radium? At equilibrium, in a sealed container, uranium activity equals radon activity.

Determine the mass of uranium-238 in a volume that has 50 ppm uranium. Determine uranium-238 activity from uranium-238 specific activity. Radon activity = uranium-238 activity.

If there is no equilibrium of progeny to uranium, then determine radium-226 activity. Equilibrium must be established in a sealed container.

But there are different equations depending upon the decay constant X1>X2 or X2

The equation to use is for secular equilibrium, because X1>>X2. 

Do you have information on the activity of U-238 and Ra-226?

No, I don't know their activities. Actually, I was reading publications on formation of radon halo on hydrocarbon (HC) reservoir. I was just thinking how much radon form from the decay of uranium that such a significant radon value is obtain in the halo zones. Uranium concentration is most rocks stay between 50 to 100 ppm. Though in actual case its an open system, so the equilibrium equation doesn't work. But for rough estimation, I will use this equation.

So in equilibrium,

N1X1=N2X2=N3X3, 

i.e. N1X1=N3X3

where N1= not decay atoms of uranium at a given time, N2= not decay atoms of radium, N3= not decay atoms of radon. X1, X2, X3 are the decay constant of uranium-238, radium-226, radon-222.  From the half-life, i will find out the decay constant. But I am now wondering, though it could be  a silly question. Do, I need to find out how many atoms of uranium is there in 50ppm of uranium as in the equation, N is the number of atoms. Or I can directly consider N= concentration in ppm?

The better estimate of activity is from number of atoms. The number of atoms calculated will depend on the expression of ppm. Ppm could be expressed as mass, volume, or atoms. 

Subsurface material is assumed in equilibrium, unless there is high porosity and high flow in the pores. The radon concentration will be near equilibrium with high flow as most radon remains in the grains.

This may help you.  1 ppm U-238 corresponds to 12.5 Bq/kg U-238. Therefore, 50 ppm U-238 is equivalent with an activity concentration of 625 Bq/kg U-238. 

To be frank, our questioner should've known the answers from school. The helpers did the right thing and helped him. What I'm interested in what Sde De means "by radon halo on hydrocarbon (HC) reservoir", and by "radon value is obtain in the halo zones". Is it in the minerals? Is it alpha halos? How do you define such "halo"?

assuming equilibrium conditions: 1ppm U= 12.4 Bq/kg or Bq/Liter, then 50ppm of U equivalent to  produce 625 Bq U ~ 625 Bq Ra-226 ~ 625 Bq radon-222

Hannu Arvela (Sir) & E. M. El Afifi (Sir) . thank you for your response. I am bit late to respond. I may write back here, once I actually solve it. 

Joseph L Alvarez (Sir) thank you so much. 

We can calculate the radon production rate P (Bq/ (h kg)  using the following equation. In other words, P   is the radon production rate (Bq/h)  from one kg  of this material.

P = lamb x E x  A, where lamb is the decay constant of Rn (ln2 / (3.8 x 24h) = 0.0076 1/h,  E is emanation coefficient of Radon (0.3,   assumed) and A  is activity concentration of this material (625 Bq/kg)

The equation gives 0.0076 x 0.3 x 625 Bq/ (h kq) = 1.4 Bq/ (h kg) 

The emanation factor (typically 0.1 - 0.3) tells, that the fraction of 0.3 from the radon created escapes from the solid matrix to the free mineral pore air filled volume.

For example, in an apartment built  using this mineral material as the concrete ballast material, the total radon production rate would result in an indoor radon concentration of  300 Bq/m3 (rough estimate, an air exchange rate of 0.5 1/h assumed)

Best regards, Hannu Arvela

Hanna Arvela (Sir), just search on radon-geology, few days back,  I came across the following reference:

Otton, J. K. (1992). The geology of radon. USGS Publications Warehouse.

In this book, they have mentioned that only 10 to 50% of radon produce can escape from the mineral matrix. And they have shown a diagram where there is critical area inside the mineral, from where the radon can escape.

This question of emanation was juggling in my mind. Honestly, I was not aware of the emanation factor term. I will now look for that, though you have mentioned the factor value. If it is possible you can please also share some references. Thank you very much for this valuable response.

calculations give only  the maximum value of emitted radon considering 1. equilibrium  2. 100% emanation power of the used uranium sample 3. no leakage of radon from the container  . because of radon is a gas you have to measure it  and then calculate both the emancipation power (characterize the source) and the leakage rate (characterize the container )

Establish the equilibrium condition between U with its daughters, i.e., Ra-226, Rn-222..

convert ppm U to Bq/kg (1mg U ~ 12.4 Bq)

Assume the equilibrium condition, then: A(U) = A(Rn)

At equilibrium (circular) activity of uranium is same as those of its daughters. Rn exhalation can be obtained from the activity of Ra depending on sample matrix.