Question

C. Half life 67Ga is 78 h. How long will it
take to decay 12% of sample of Ga ?​

Answer 1

Using formula of half life , T = ln2/λ

where λ is decay constant.

so, 78 hrs = ln2/λ

⇒λ = ln2/78 ≈ 0.00888 hour^-1

as radioactive decay is a first order reaction.

so, rate of decay is given as,

t = 2.303/λ log[A/At]

where A is initial amount of substance (Ga)

At is final amount of substance = A - 12% of A = A - 0.12A = 0.88A

so, t = 2.303/0.00888 log[A/0.88A]

= 2.303/0.00888 log(1/0.88)

= 33.1352 hours

hence, 33.1532 hours take to decay of sample of Ga.

Answer 2

$\huge\bold\purple{Answer:-}$

Using formula of half life , T = ln2/λ

where λ is decay constant.

so, 78 hrs = ln2/λ

⇒λ = ln2/78 ≈ 0.00888 hour^-1

as radioactive decay is a first order reaction.

so, rate of decay is given as,

t = 2.303/λ log[A/At]

where A is initial amount of substance (Ga)

At is final amount of substance = A - 12% of A = A - 0.12A = 0.88A

so, t = 2.303/0.00888 log[A/0.88A]

= 2.303/0.00888 log(1/0.88)

= 33.1352 hours