Can half-life be negative?

It has a negative sign because the number of nuclei of the isotope will decrease over time. The rate of decay is equal to the number of the nuclei multiplied by a proportionality constant that depends on the exact isotope.

butane.chem.uiuc.edu - Rate and Half-Life

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Rate and Half-Life

Half-Life of Isotopes We have seen that many isotopes of the elements are unstable with respect to loss of a neutron, alpha particle, or beta particle. All of the heavy elements are thermodynamically less stable than their constituent particles and can undergo fission. The amount of time it takes for 1/2 of the sample to decompose is called the half-life. This varies considerably from isotope to isotope. The mode of radioactive decay also varies. For example, plutonium-239 emits alpha particles and plutonium-242 emits beta particles. Both isotopes also produce gamma rays. isotope half life isotope half life 3H 12.3 y 20F 11.4 s 14C 5730 y 24Na 15.0 h 32P 14.3 d 35S 88 d 36Cl 3.1 x 105 y 40K 1.28 x 109 y 45Ca 165 d 59Fe 45 d 60Co 5.26 y 82Br 35.5 h 90Sr 28 y 129-I 1.7 x 107 y 131I 8.1 d 137Cs 30 y 198Au 2.69 d 226Ra 1.62 x 103 y 235U 7.1 x 108 y 238U 4.51 x 109 y 239Pu 2.44 x 104 y 241Pu 14.4 y Kinetics of Radioactive Decay The rate of nuclear reaction depends only on the isotope and the quantity of material present. Lets call the number of nuclei of a particular type N. The rate of decay of this isotope can be represented by - N/ t, or the change in the number of this kind of nuclei per change in time. It has a negative sign because the number of nuclei of the isotope will decrease over time. The rate of decay is equal to the number of the nuclei multiplied by a proportionality constant that depends on the exact isotope.

We can integrate this expression:

The graph on the left below shows the decrease in the number of the radioactive nuclei, N, over time. When the -ln(N) is plotted versus time, the plot (right) is a straight line with a slope equal to the rate constant and an intercept on the y axis equal to the initial number of nuclei. It can be useful to rearrange the rate expression above in order to calculate the time it takes for some fraction of the material to decompose. When 1/2 decomposes the ratio of initial nuclei to remaining nuclei is 2, ln(N 0 /N) = ln(2) = 0.693. The time required for this is 0.693/ k . An applet by W. Bauer shows the decay of radioactive nuclei as a function of the half-life.

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Does K decrease with temperature?

The temperature will affect the value of K. If the temperature is increased in an endothermic reaction, K will increase but in an exothermic reaction K will decrease. This is because by raising the temperature in an endothermic reaction, you are favoring the creation of the products for that reaction.

lavelle.chem.ucla.edu - How Does Temperature Affect the Equilibrium Constant?

Postby Eliana Carney 3E » Sun Jan 31, 2021 6:28 pm

Hey Lilyana!

Basically, if the reaction is endothermic, then heating will favor product formation and increase K. If the reaction is exothermic, then heating will favor reactant formation and decrease K. I like to think of heat as either a product or a reactant depending on the reaction, and this helps me understand and remember the changes in K. For endothermic reactions, heat acts like a reactant because it is needed to form products, so increasing heat would be like increasing the concentration of a reactant and we know that this causes the formation of products. Therefor, when heat is added to an endothermic reaction, the K value increases because there is more products at equilibrium. The same thing goes for exothermic reactions. In exothermic reactions, heat acts like a product because it is released, so increasing heat would be like increasing the concentration of a product, which would cause the formation of reactants. The formation of reactants would cause the value of K to decrease. Hope this helps!

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