Question

Q.1 Radioactive 68Ge decays by β+ with a 271 day half-life. How many grams of an initial 2.50 g sample of 68Ge remain after 365 days of radioactive decay?

Q.2 A particular reaction has an initial concentration of 4.302 M and a final concentration of 3.978 M after 1.08 seconds. The rate constant is 0.0175 M-1s-1. What is the half-life at the initial concentration?

Answer #1

Q. 1

As radioactive substances follow 1st order reaction kinetics

So. the amount remain N = No(1/2)^{n}

where N = final amount after n^{th} half life (ie.
t^{1/2}) and No = initial amount

Here, No = 2.5g and n = 365/271 = 1.34685

so, N = 2.5(1/2)^{1.34685}

So the value of 2.5/2^{1.34685} will give the amount
left after 365 days.

Q.2: The unit of rate constant (M^{-1}s^{-1})
show about the type of reaction kinetics ie. 2nd order

So, For 2nd order t^{1/2}_{=}
1/a.k_{2}

where, a = initial concentration and k_{2} rate
constant

from eq. t^{1/2}_{=} 1/4.302 x 0.0175

= 13.28 sec. is the half life.

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