Rate of emission of alpha particle in uranium decay

[songoku]

Homework Statement

U - 238 is undergoing alpha emission into Th - 234. U - 238 has half – life of 10⁹ years. Calculate the emission rate of alpha when uranium has mass of 10 grams

Homework Equations

A = λN
A = A₀ (1/2)ⁿ , n = t / half - life

The Attempt at a Solution

Not sure how to do it but here is my attempt:

Rate of emission of alpha = rate of decay of uranium = activity of uranium.

mass = 10 gram --> number of particle of uranium = 10/238 x 6.02 x 10²³ = 2.529 x 10²²

half - life = 10⁹ years = 3.154 x 10¹⁶ s

A = ln 2 / (3.154 x 10¹⁶) x 2.529 x 10²² = 5.56 x 10⁵ Bq

Is this correct? Thanks

 

[mfb]

The given half life is wrong, but if you use this wrong value it is correct.

 

[songoku]

I searched through google and found out that the half - life should be 4.468 x 10⁹ years. So I only need to change the value of half - life.

Thank you mfb