Question

The half life of a radioactive substance is 69.3 minutes how much time will it take to dissing plate 80% of his

Answer 1

The half life of a radioactive substance is 69.3 minutes how much time will it take to dissing plate 80% of ...

solution : The half life of radioactive substance is given by, $T=\frac{ln2}{\lambda}$

where , λ is decay constant and T is half life.

given, T = 69.3 minute

so, 69.3 = ln2/λ

or, λ = ln2/69.3 = 0.693/69.3 = 10^-2 /min [ as we know, ln2 = 0.693 ]

now a/c to question

we have to find time taken to 80% of decay radioactive substance.

if we assume N is initial amount of substance then, final amount of substance , N' = N - 80% of N = 0.2N

using formula, N' = Ne^{-λt}

or, 0.2N = Ne^{-10^-2t}

or, 0.2 = e^{-10^-2t}

or, ln(0.2) = -10^-2 t

or, t = -ln(0.2)/10^-2 = -1.6/-10^-2 = 160 minutes

hence, time taken = 160 minutes.

Answer 2

Hii Dear,

◆ Answer -

t = 160.9 min

◆ Explanation -

# Given -

λ = 69.3 min

A' = (100-80)% A = A/5

# Solution -

Amount of radioactive substance after time t is -

A' = A e^(-λt)

A/5 = A e^(-λt)

e^(-λt) = 1/5

Taking log on both side -

-λt = log(1/5)

-0.693/t½ × t = log(1/5)

-0.693/69.3 × t = -1.609

t = 1.609 × 100

t = 160.9 min

Therefore, it will take approx 161 min to disintegrate 80% of the substance.

Thanks.