The half life of radioactive radon is 3.8 days . The time , at end of which 120th of radon sample will remain undecayed is
Answers
1/20th sample will remain undecayed
so decay = 1 - 1/20
= 19/20
= 95 % decay
100/2 = 50 % decay = 3.8 days
remaining = 100 - 50 = 50%
50/2 = 25 % decay = 3.8 days Total decay = 75% , Total days = 7.6 Days
remaining = 50 - 25 = 25%
25/2 = 12.5 % decay = 3.8 days Total decay = 87.5% , Total days = 10.4 Days
remaining = 50 - 12.5 = 12.5%
12.5/2 = 6.25 % decay = 3.8 days Total decay = 93.75% , Total days = 15.2 Days
remaining = 12.5 - 6.25 = 6.25%
6.25/2 = 3.125 % decay = 3.8 days Total decay = 96.875% , Total days = 19 Days
remaining = 6.25 - 3.125 = 3.125%
Approx in 16.5 days it will remain 1/20th
or we can use
formula
N(x) = N₀eᵃˣ
x = time
a = constant
a = ln(1/2) / 3.8
=> a = -0.693/3.8
=> a = -0.182
N(x) = N₀/20
ln(1/20) = -0.182x
=> -3 = -0.182x
=> x = 16.48 Days