Atoms and Nuclei Part 1

From equation of radioactivity we know At=A0e−λt
Where At= Amount of material at time 't'
A0= Amount of substance at t=0
λ= decay constant
t= time.
Taking log we have ln[‌

A0

At

]=λt
For half life At=‌

A0

2

.
⇒ln‌2=λt1∕2‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(A)
t1∕2= half life
From given condition.
ln[‌

700

500

]=λ(30‌min)‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(B)
(A)−(B)
‌

ln‌2

ln[7∕5]

=‌

t1∕2

30

⇒t1∕2=‌

ln‌2×30

ln[7∕5]

⇒t1∕2=‌

0.693×30

0.336

⇒t1∕2=61.8min
‌ option (d) is correct. ‌