Question

Question 1. What is the final product of the radioactive decay of ²³⁸U? The successive radiation processes are: α, β, β, α, α, α, α, α, β, β, α, β, β, α.

Question 2. Rutherford and Geiger determined that α-particles were emitted from Ra-224 at a rate of 7.65×10¹² s^-1 .mol^-1,and that this corresponded to a rate of He production of 2.90×10^-10 L.s^-1 at 273 K and 1 bar. Estimate the value of Avogadro’s number using his information – as well as anything else you might know about an ideal gas.

Answer 1

There are multiple questions here . i am allowed to answer only 1 at a time. I will answer 1st one for you. Please ask other as different question

1)
Atomic number of U = 92 and mass number is 238

In alpha decay atomic number decreases by 2 and mass number decrease by 4
Total number of alpha decay = 8
decrease in mass number = 8*4 = 32
decrease in atomic number = 8*2 = 16

In Beta decay atomic number incraeses by 1 and mass number doesn't change
Total number of Beta decay = 6
increase in atomic number = 6*1 = 6

Net decrease in mass number = 32
Net decrease in atomic number =16 -6 = 10

For final product:
atomic number = 92 - 10 = 82 (This corresponds to lead, Pb)
mass number = 238 - 32 =206
So, final product is 206Pb