Question

show that mass of radium (88Ra²²⁶)with a activity if 1 curie is almost a gram​ given T1/2 =1600 years

Answer 1

Answer:

Activity = dNdtdNdt 1 curie = 3.7×10103.7×1010 disinetegration per second , Half life of Radium = 1600 years

λ=0.6391T1/2,λ=0.69311600λ=0.6391T1/2,λ=0.69311600 per year

=0.69311600×365×24×60×60=0.69311600×365×24×60×60 per second

From law of disintegration

dNdt=λN,N=dNdt×1λdNdt=λN,N=dNdt×1λ

dNdt=3.7×1010dNdt=3.7×1010 disintegrations/second

∴N=3.7×1010×16000.6931×365×24×60×60∴N=3.7×1010×16000.6931×365×24×60×60

= 3.7×1010×1.443×1600×365×24×60×603.7×1010×1.443×1600×365×24×60×60

N=2.694×1021N=2.694×1021 atoms

According to Avogadro.s principle

Mass of 6.023×10236.023×1023 atoms give : 226 gm of radium

∴∴ Mass of 2.694×10212.694×1021