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Question

# The masses of two radioactive substances are same and their half lives are 1 year and 2 years respectively. The ratio of their activities after 6 years will be1:41:61:21:3

A
1:4
B
1:6
C
1:2
D
1:3
Solution
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#### Given : TA=1 years and TB=2 years Time of observation t=6 yearsLet the initial mass (or nuclei) of two radioactive substance be No.Initial activity of substance A RoA=λANo=(ln2)NoTAActivity of substance A after time t, RA=RoAe−(ln2)tTAInitial activity of substance B RoB=λBNo=(ln2)NoTBActivity of substance B after time t, RB=RoBe−(ln2)tTBThus ratio of activities after 6 years, we get RARB=RoARoBe−(ln2)[tTA−tTB]Or RARB=TBTAe−(ln2)[61−62]Or RARB=21e−3ln2=2×eln18Or RARB=2×18⟹ RA:RB=1:4

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