Q2 (c) 92238U is radioactive and it emits a and b particles to form 82206Pb Calculate the number of - Chemistry - Chemical Kinetics

Question

Q2 (c) 92238U is radioactive and it emits a and b particles to form
82206Pb Calculate the number of a and b particles emitted in this
conversion An ore of 92238U is found to contain 92238U and 82206Pb
in the weight ratio of 1:0 1 The half-life period of 92238U is 4 5
x 10 9 years Calculate the age of the ore

Vartika Jain · Accepted Answer

Dear Student,

Let 'a' and 'b' be the number of α and β particles emitted during the change92U238 → 82Pb206 + a 2He4 + b -1e0Comparing the mass numbers, 238=208+4a+(b×0)4a=238-2064a=32a=324=8Comparing the atomic numbers92=82+2×a+(-1)b    =82+2a-b2a-b=92-82          =102(8)-b=10b=16-10=6Number of α-particles emitted=8Number of β-particles emitted=6N0 = 1238+0
1206=46 85×10-4 moleN=1238= 42
0×10-4 moleλ=0 693t=0 6934 5×109=1
54×10-9 year-1As we know, t=2
303λlog N0N =2 3031 54×10-9log 46
85×10-442 0×10-4 =7 097×108 year