A) \[{{a}_{0}}{{t}_{0}}\]In \[(2)\]
B) \[\frac{{{a}_{0}}{{t}_{0}}}{In\,(2)}\]
C) \[{{a}_{0}}{{t}_{0}}\]
D) \[\frac{{{a}_{0}}{{t}_{0}}}{2}\]
Correct Answer: B
Solution :
[b] Comparing this with radioactive disintegration. The disintegration constant is \[\lambda =\frac{\ell n(2)}{{{t}_{0}}}\] and \[a={{a}_{0}}{{e}^{-\lambda t}}\] or \[\frac{dv}{dt}={{a}_{0}}{{e}^{-\lambda t}}dt\] or \[\int\limits_{0}^{{{v}_{r}}}{dv\,\,=\,\,{{a}_{0}}}\int\limits_{0}^{\infty }{{{e}^{-\lambda t}}dt}\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,{{v}_{T}}=\frac{{{a}_{0}}}{\lambda }=\frac{{{a}_{0}}{{t}_{0}}}{\ell n(2)}\]
You need to login to perform this action.
You will be redirected in
3 sec
