Given a sample of Radium-226 having half-life of 4 days. Find the probability, a nucleus disintegrates after 2 half lives.

Question

Given a sample of Radium-226 having half-life of 4 days. Find the probability, a nucleus disintegrates after 2 half lives. (A) 1 (B) 1/2 (C) 1.5 (D) 3/4

Tardigrade Admin · Accepted Answer

The probability for the decay is 1-e-λ t t =2 t(1/2)=2((l n2/λ)) . Therefore, P (decay) =1-e-λ (2( ln 2)/λ) =1-e-l n 4=1-(1/4)=(3/4)

Q. Given a sample of Radium- $226$ having half-life of $4$ days. Find the probability, a nucleus disintegrates after $2$ half lives.

1

1/2

1.5

3/4

The probability for the decay is
$1 - e^{- λ t}$
$t = 2 t_{\frac{1}{2}} = 2 (\frac{l n _{2}}{λ}) .$
Therefore,
$P$ (decay) $= 1 - e^{- λ \frac{2 ( l n 2 )}{λ}}$
$= 1 - e^{- l n 4} = 1 - \frac{1}{4} = \frac{3}{4}$

Q. Given a sample of Radium-226 having half-life of 4 days. Find the probability, a nucleus disintegrates after 2 half lives.

1

1/2

1.5

3/4

The probability for the decay is 1−e−λt t=2t21​​=2(λln2​​). Therefore, P (decay) =1−e−λλ2(ln2)​ =1−e−ln4=1−41​=43​

Q. Given a sample of Radium- $226$ having half-life of $4$ days. Find the probability, a nucleus disintegrates after $2$ half lives.

The probability for the decay is
$1 - e^{- λ t}$
$t = 2 t_{\frac{1}{2}} = 2 (\frac{l n _{2}}{λ}) .$
Therefore,
$P$ (decay) $= 1 - e^{- λ \frac{2 ( l n 2 )}{λ}}$
$= 1 - e^{- l n 4} = 1 - \frac{1}{4} = \frac{3}{4}$