Name: Liquid Drop Model of Nucleus
Uploaded: 2019-07-19
Duration: 2 min 42 s
Description: Did you know a liquid drop shares many similarities with a nucleus? It will be interesting to learn the similarities let's learn the liquid drop model of the...

Question

{}^{90}{Sr}

decays to

{}^{90}Y

by

β

decay with a half-life of

28 years

.

{}^{90}Y

decays by

β

decay to

{}^{90}{Zr}

with a half-life of

64 h

. A pure sample of

{}^{90}{Sr}

is allowed to decay. What is the value of

\frac{N_{Sr}}{N_{Y}}

after

(a)

1 h

(b)

10 years

?

Accepted Answer

As we know that number of radioactive atoms at time $t$ for $Sr$ and $Y$ is given by,

$β$ (where $e$ is Euler's number and $λ_{Sr}$ is the decay constant of $Sr$ )

$N_{Y} = \frac{λ_{Sr} N_{Sr}^{0}}{λ_{Y} - λ_{Sr}} [e^{(- λ_{Sr} t)} - e^{(- λ_{Y} t)}] . . . (2)$ (where $λ_{Y}$ is the decay constant of $Y$ )

Dividing equation $(2)$ from equation $(1)$ ,

$\frac{N_{Y}}{N_{Sr}} = \frac{λ_{Sr}}{λ_{Y} - λ_{Sr}} [1 - e^{(- t) (λ_{Sr} - λ_{Y})}] . . . (3)$

$∵$ Half life of decay from ${}^{90}{Sr}$ to ${}^{90}Y$ is $28 years$ ,

i.e., $λ_{Sr} = \frac{0.693}{28 \times 365 \times 24}$

$\Rightarrow λ_{Sr} = 2.825 \times 10^{- 6} h^{- 1}$

and half life of decay from ${}^{90}Y$ to ${}^{90}{Zr}$ is $64 h$ ,

i.e., $λ_{Y} = \frac{0.693}{64}$

$\Rightarrow λ_{Y} = 0.0108 h^{- 1}$

$(a)$ For ratio of number of radioactive atoms at time, $t = 1 h$ , putting value of $λ_{Sr}$ and $λ_{Y}$ in equation $(3)$ , we get,

$\frac{N_{Sr}}{N_{Y}} = \frac{0.0108 - 2.825 \times 10^{- 6}}{2.825 \times 10^{- 6} [1 - e^{- 1 (2.825 \times 10^{- 6} - 0.0108)}]}$

$\Rightarrow \frac{N_{Sr}}{N_{Y}} = 3.56 \times 10^{5}$

$(b)$ For ratio of number of radioactive atoms at time, $t = 10 year s = 10 \times 365 \times 24 = 87600 h$ , putting value in equation $(3)$ , we get,

$\frac{N_{Sr}}{N_{Y}} = \frac{0.0108 - 2.825 \times 10^{- 6}}{2.825 \times 10^{- 6} [1 - e^{- 87600 (2.825 \times 10^{- 6} - 0.0108)}]}$

$\Rightarrow \frac{N_{Sr}}{N_{Y}} = 3823$

${}^{90}{Sr}$ decays to ${}^{90}Y$ by $β$ decay with a half-life of $28 years$ . ${}^{90}Y$ decays by $β$ decay to ${}^{90}{Zr}$ with a half-life of $64 h$ . A pure sample of ${}^{90}{Sr}$ is allowed to decay. What is the value of $\frac{N_{Sr}}{N_{Y}}$ after $(a)$ $1 h$ $(b)$ $10 years$ ?

Important Questions on Nuclear Physics

Learn and Prepare for any exam you want !

Sr90 decays to Y90 by β decay with a half-life of 28 years. Y90 decays by β decay to Zr90 with a half-life of 64 h. A pure sample of Sr90 is allowed to decay. What is the value of NSrNY after a 1 h b 10 years?

Important Questions on Nuclear Physics

Learn and Prepare for any exam you want !

${}^{90}{Sr}$ decays to ${}^{90}Y$ by $β$ decay with a half-life of $28 years$ . ${}^{90}Y$ decays by $β$ decay to ${}^{90}{Zr}$ with a half-life of $64 h$ . A pure sample of ${}^{90}{Sr}$ is allowed to decay. What is the value of $\frac{N_{Sr}}{N_{Y}}$ after $(a)$ $1 h$ $(b)$ $10 years$ ?