The half life of radioactive radon is 3.8 days

Asked by admin @ 17/08/2021 in Physics viewed by 281 People

The half life of radioactive radon is 3.8 days . The time , at end of which 120th of radon sample will remain undecayed is

Answered by admin @ 17/08/2021

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

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