The correct option is B 12 h
Let's say the permissible level is N, so initially we have 64N nuclei present.
We need to calculate the time taken to drop the number of nuclei from 64N to N.
We know, N = N0e−λt
N0 is 64N here. So after subtituting this we get,
e−λt=164
Or,
eλt=64.
Which gives,
λt=In 64.
Or,
t=In 64λ………1)
Now we have half-life,t1/2 = 2h
Which gives, λ = In 2t1/2= In 22h
Now putting this value in equation 1)
t = In 64λ=In 64In 2×2h
Or,
t = 6 In 2In 2×2h=12h.