The half-life of a radioactive isotope is the amount of time it takes for a quantity of that isotope to decay to one half of its original value. (a) express the half-life of a radioactive isotope in terms of its decay rate. (b) the half-life of radiocarbon or carbon 14 (c-14) is 5230 years. determine its decay rate parameter . (c) carbon dating is a method of determining the age of an object using the properties of radiocarbon. it was pioneered by willard libby and collaborators in 1949 to date archaeological, geological, and other samples. its main idea is that by measuring the amount of radiocarbon still found in the organic mater and comparing it to the amount normally found in living matter, we can approximate the amount of time since death occurred.7 using the decay-rate parameter found in part (b), nd the time since death if 35% of radiocarbon is still in the sample.

Radio active decay reactions follow first order rate kinetics.

a) The half life and decay constant for radio active decay reactions are related by the equation:

Where k is the decay constant

b) Finding out the decay constant for the decay of C-14 isotope:

c) Finding the age of the sample :

35 % of the radiocarbon is present currently.

The first order rate equation is,

t = 7923 years

Therefore, age of the sample is 7923 years.

values of the quantum numbers: -6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6

location of the electron: In the 7th energy level away from the nucleus.

Explanation:

From the description of the problem, the magnetic number is given is as -6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6 and the electron is located in the 7th energy level away from the nucleus. Basically, the problem is testing for the understanding of the principal quantum numbers which gives the location of electrons and the magnetic quantum number that shows the spatial orientation of the orbitals.

           The orbital designation of the describe electron is 7d

Magnetic quantum number is limited by the azimuthal quantum number which is the quantum number describing the possible shapes. The azimuthal is given as L= n-1. "n" is the principal quantum number which is 7. Therefore L is 6 and the magnetic quantum numbers are -6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6

The position of the electron is given by the principal quantum number which represents the main energy level in which the orbital is located or the average distance from the nucleus.

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