Radiogenic isotopes are isotopes produced by the decay of radioactive parent isotopes. Some common radiometric dating methods include: 1. Uranium-lead dating, which measures the decay of uranium isotopes to lead isotopes. 2. Potassium-argon dating, which measures the decay of potassium-40 to argon-40. 3. Rubidium-strontium dating, which measures the decay of rubidium-87 to strontium-87. These and other radiometric dating techniques, such as carbon-14 dating, are used to determine the age of rocks and minerals based on the decay of radioactive isotopes into radiogenic daughter isotopes

1. TOPIC-RADIOGENIC ISOTOPE NAME-SRIDHARA SAHU
RAVENSHAW UNIVERSITY MSC -2ND YR(IV SEMI)
ROLL NO-15-MGL-008

2. RADIOGENIC ISOTOPE
INTRODUCTION:
• Atom is a fundamental unit of matter. Made up of components called
subatomic particles
1. Proton (positive charge)
2. Neutron (no electrical charge)
3. Electron (negative charge)
• Nucleus contains protons and neutrons, contains most of the mass of
the atom, electrons are distributed around the nucleus in shells and
orbitals.
• Mass Number (A) is a total number of protons and neutrons in the
nucleus.
• Atomic Number (z) reflects a total number of protons in the nucleus

3. mass number (proton + neutron ) A
z X element
atomic number (protons)
 Number of neutron= mass number(A) – atomic number(Z)
 Isotopes of certain element have the same number of protons (p+) but
distinct number of neutrons (n0).Isotopes are atoms of the same element
having different masses.

4. RADIOGENIC ISTOPE:
 An isotope which was produced by the decay of a radioisotope, but which itself
may or may not be radioactive.
 Radioactive isotope also called radioisotope, radionuclide or radioactive
nuclide any of several species of the same chemical element with different masses
whose nuclei are unstable and dissipate excess energy by spontaneously
emitting radiation in the form of alpha, beta, and gamma rays.
 Alpha (α)–emission of two neutrons and two protons together as helium ion
from nucleus
A
ZX A-4
Z-2X+ α +Energy
 Beta (β)–emission of electron from nucleus resulting in increase in atomic
number of 1 in original nucleus.
1. Negative ( β) particle: 87
37Rb 87
38Rb+β-
2. Positive ( β) particle: 10
6C 10
5C + β+

5.  Gamma (γ)–emission of photons from excited nuclei.
A
ZX A
ZX + γ +Energy
Law of Radioactivity: Rutherford and Soddy (1902) discovered that the rate of decay of a
radioactive nuclide (N) at any instant is proportional to the number of atoms of the nuclide
remaining at that instant:
-dN/dt = λN
Where λ is decay constant and the negative sign (-) indicate that the amount of radioactive
nuclide (N) decreases with time(t). The decay constant (λ) and this is not affected by changes
in the temperature, pressure, and chemical reactions.

6. Decay Curves for Radioactive Isotopes:
1. Exponential Decay Curve :
N=N0e –λt
Where N0 represents the initial number of radioactive parent atoms and e is the
base of natural logarithm (e=2.71828).
2.Complementary Growth Curve:
D*=N0(1-e-λt)
where D*represents the generation of stable daughter isotopes created by radioactive
decay of No isotopes.

7. Half-life (T1/2): The half-life is defined as the time required for one half of a given number of the
radioactive atoms to decay.
Substituting this in equation of exponential Decay Curve
N=N0e –λt
Then we obtain the following relation
NO/2=NO e –λ T1/2
Hence T1/2=ln2/ λ =0.693/ λ
Thus, if t=T1/2ThenN=NO/2

8. Isotope Based Geochronology: The relationship between the radiogenic
daughter isotopes (D*) and the remaining radioactive parents (N) can be
expressed as: D*=N (e λt-1)
This equation is practical as both isotope parameters (D*and N) are measurable,
quantites and thus it represents the basis for the isotope geochronology used to
determine the age of mineral/rock formation.
However for realistc age calculations we have to consider the total number of
radiogenic daughters (D) based on:
D=D0+D*
Where (D0) is the initial number of daughters present in the sample at
the time of its formation and (D*) is the number of daughters
produced by decay.
Thus, D=D0+N(e λt-1) (General equation for age determination)

9. DIFFERENT METHOD:

10. a. uranium-lead method: Uranium has two radioactive isotopes that each
decay to different lead isotopes
238U → 206Pb+ 8He4; λ238,1.551 × 10–10 a–1; half-life 4468 Ma
235U → 207Pb+7H4; λ235, 9.849 × 10–10 a–1; half-life 704 Ma
Though both parents belong to the same element, as do both daughters, their decays
are quite independent, and each daughter/parent ratio can be used in the Basic Dating
Equation, with the appropriate decay constant.
As an example, suppose the 206Pb/238U ratio is 1.562 × 10–2.
0.01562=(eλt-1)
The U–Pb method can be applied to a number of minerals, including sphene, uraninite,
monazite, and apatite.
b. The potassium–argon (K–Ar): This, probably the most used single method, has two versions,
the ‘conventional’ potassium–argon (40Ar/40K) and the argon–argon (40Ar/39Ar) methods, with
the term ‘potassium–argon method’ referring to either method.

11. 40K → 40Ar (+40Ca); λ, 5.543 × 10–10 a–1; half-life, 1250 Ma
40Ar/40K=0.105(eλt-1)

12. C. The argon–argon (Ar–Ar) method
In this variant of the K–Ar method, the sample is first irradiated with fast neutrons in a nuclear pile, which
converts a measured proportion, p, of the 39K atoms into 39Ar atoms:
40K 40Ar 39Ar
Decay irradiation
As the ratio of 39Ar to 39K atoms is p, and as the ratio of 40K to 40Ar in potassium is known, by measuring 39Ar is
equivalent to measuring 40K, and so we can replace 40K in Eq. by 39Ar:
d. The rubidium–strontium (Rb–Sr) method:
There are several isotopes of rubidium and strontium, but the ones relevant to dating are
87Rb → 87Sr; λ87, 1.42 ×10–11 a–1; half-life, 48,800 Ma
86Sr (reference isotope, not formed by decay)
The value of 87Sri, varies from one mineral to another, so we divide by 86Sr to provide a ratio that was the same
everywhere when the rock first crystallised:

13. As the amount of the reference isotope 86Sr does not change, we can regard it as either 86Sri or 86Srnow as it suits us. The
equation can be rewritten as
This is the equation of a straight line, which has the form y = mx + c (Fig-b); m is the slope of the line and c is the value of y
when x is zero, that is, (87Sr/86Sr)i.

14. e. The samarium–neodymium (Sm–Nd):
This is similar to the Rb–Sr method, for there are several isotopes of both elements and the daughter, Nd, is present at closure
and so an isochron is needed.
The relevant isotopes are
147Sm → 143Nd; λ147, 6.54 × 10–12 a–1; half-life, 1.06 × 105 Ma
144Nd (reference isotope)
Comparison with the Rb–Sr method shows that 147Sm corresponds to 87Rb, 143Nd to 87Sr, and 144Nd to 86Sr. Substituting these values in Eq. 2 gives
The method is more applicable to basic and ultrabasic rocks. Because of the extremely long half-life of 147Sm, the 143Nd/144Nd
ratio evolves slowly, so the method is mainly applied to old rocks, often thousands of millions of years old, including some
meteorites.
f. The lead–lead (Pb–Pb) dating method:
238U → 206Pb; λ238; 1.551 × 10–10 a–1; half-life, 4468 Ma
235U → 207Pb; λ235, 9.849 × 10–10 a–1; half-life, 704 Ma
235U → 204Pb (reference isotope)
Most rocks and minerals that contain uranium also have lead present initially , so we use isochrons analogous to
that for the Rb–Sr method :

15. Though the actual quantities that vary, y and x, are (207Pb/204Pb)now and (206Pb/204Pb)now, the equation is
simpler if we regard the whole brackets yr and xr, as the variables, for then it is simply the equation of a straight
line with slope m. The variables yr and xr are the increases in the ratios since closure; in effect, we have shifted
the origin (0, 0) of the plot to the point defined by the initial lead isotopic ratios, I
g. Rhenium-osmium:
 Rhenium and osmium are siderophile elements which are present at very low abundances
in the crust.
 Rhenium undergoes radioactive decay to produce osmium. The ratio of non--
radiogenic osmium to radiogenic osmium throughout time varies.

16. h. lu-hf method:
The Lu-Hf system is in many respects similar to the Sm-Nd system:
(1) in both cases the elements are relatively immobile;
(2) in both cases they are refractory lithophile elements; and
(3) in both cases the daughter is preferentially enriched in the crust, so both 143Nd/144Nd and
176Hf/177Hf ratios are lower in the crust than in the mantle.
 Rhenium prefers to enter sulfides more readily than osmium. Hence, during melting of the
mantle, rhenium is stripped out.
As they did for the Sm-Nd system, geochemists found it useful to define εHf as the relative
deviation in parts by 104 from the chondritic value. εHf is calculated as

17. i. carbon dating:
Radiocarbon dating (also referred to as carbon dating or carbon-14 dating) is a
method for determining the age of an object containing organic material by using
the properties of radiocarbon (14. C), a radioactive isotope of carbon.
Carbon has two stable isotopes, 12C and 13C, and one radioactive isotope, 14C.
Radioactive Decay: The nucleus of an atom (decays) changes into a new element
The proton number (atomic number) changes
 The half-life of C-14 is 5,730 years.

18. How carbon is produced:
Carbon-14 life cycle:
Carbon-14 is produced in the atmosphere
Carbon-14 decays into Nitrogen-14

19. When Does the Clock Start?
Once a plant or animal dies the clock starts
How the Carbon Clock Works:
• There is a lot of C-14 remaining in the fossil
• There is very little C-14 remaining in the fossil
• There is no detectable C-14 in the fossil