English
Hindi
13.Nuclei
hard

$1.9$ વર્ષ અર્ધ આયુષ્યના $Th^{227}$ માં $1$ મિલિ ક્યુરી એક્ટિવીટી પેદા કરવા કેટલા ........... $\mu g$ જથ્થો જરૂરી છે?

A

$2.125$

B

$1.206 $

C

$1.125 $

D

$1.905$

Solution

$A = 1$ મિલી ક્યુરી $= 3.7 × 10^7$ વિભંજન/સેકન્ડ

$\lambda \,\, = \,\,\,\frac{{0.693}}{T}\,\, = \,\,\frac{{0.693\,}}{{1.9\,\, \times \,365\,\, \times \,\,24\,\, \times \,60\,\, \times \,\,60}}$

એક્ટિવ પરમાણુ ની સંખ્યા $ = \,\,\frac{{6.023\,\, \times \,\,1{0^{23}}}}{{227}}\,\,m\,$

$A\,\, = \,\,\lambda N\,\,\,\, \Rightarrow \,\,\,\,\,3.7\,\, \times \,\,1{0^7}$

$ = \,\,\frac{{0.693}}{{1.9\,\, \times \,\,365\,\, \times \,\,24\,\, \times \,\,60\,\, \times \,\,60}}\,\, \times \,\,\frac{{6.023\,\, \times \,\,{{10}^{23}}}}{{227}}\,\,m$

$ \Rightarrow \,\,m\,\, = \,\, \frac{{3.7\,\, \times \,\,1{0^7} \times \,\,1.9\,\, \times \,\,365\,\, \times \,\,24\,\, \times \,\,60\, \times \,\,60\,\, \times \,\,227}}{{0.693\,\, \times \,\,6.023\,\, \times \,\,{{10}^{23}}}}\,$

$\,\,\, = \,\,1.206\,\, \, \mu \,g$

Standard 12
Physics

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