GATE-2008 (55)

GATE-2008

55. A radioactive substance decays to one third of its original value in 6 hours time. What is the half-life (in hours) of the substance?

A) 3.58

B) 3.78

C) 3.98

D)4.18

Solution:

The relation between Half-life and time

N= N₀ (1/2)^{^( t /t (1/2) )}-----------(1)

N= Nuclei present after time ‘t’ in the sample

N₀= Original Nuclei present in the sample

t_1/2- Half-life of sample

t- time

N= N₀/3 (from above problem)

N₀/3 = N₀ (1/2)^{^( 6 / t(1/2) )}

1/3 = (1/2)^{^( 6 / t (1/2) )}

log 3= log 2^ ^{( 6 / t (1/2) )}

log 3= 6 / (t_1/2) * log 2

6 / (t_1/2) = log 3 / log 2

t_1/2= 6 log 2/ log 3

t_1/2= 6 * 0.693 / 1.0986

t_1/2= 4.153 / 1.0986

Therefore Half-life(t_1/2) = 3.78

GEOPHYSICS