Radium disintegrates at an average rate of 2.24 X 10^13 alpha particles per minute. Each alpha particle takes up two electrons from the air and becomes a neutral helium tom. After 420 days, helium gas collected was 0.5 ml measured at 27 degree celcius and 750mm Hg.Calculate Avagadro constant.
(source:Modern approach to chemical calculations)

let the avagadro constant be A
number of alpha particle after 420 days =2.24*10^13*420*24*60 helium ion
=1.35*10^6*10^13 helium ion
=1.35*10^19 helium ion
now mole of helium atom
n=PV/RT
=750/760)*(.5*10^-3)/.0821*300
=2*10^-5
2*10-5 mole contain 1.35*10^19 helium atom
1 mole will have 1.35*10^19/2*10^-5
=.675*10^24
=6.75*10^23 helium atom which is the avagadro constant