<Dd> λ is the decay constant of the parent isotope, equal to the inverse of the radioactive half - life of the parent isotope times the natural logarithm of 2 . </Dd> <P> The equation is most conveniently expressed in terms of the measured quantity N (t) rather than the constant initial value N . </P> <P> The above equation makes use of information on the composition of parent and daughter isotopes at the time the material being tested cooled below its closure temperature . This is well - established for most isotopic systems . However, construction of an isochron does not require information on the original compositions, using merely the present ratios of the parent and daughter isotopes to a standard isotope . Plotting an isochron is used to solve the age equation graphically and calculate the age of the sample and the original composition . </P> <P> Radiometric dating has been carried out since 1905 when it was invented by Ernest Rutherford as a method by which one might determine the age of the Earth . In the century since then the techniques have been greatly improved and expanded . Dating can now be performed on samples as small as a nanogram using a mass spectrometer . The mass spectrometer was invented in the 1940s and began to be used in radiometric dating in the 1950s . It operates by generating a beam of ionized atoms from the sample under test . The ions then travel through a magnetic field, which diverts them into different sampling sensors, known as "Faraday cups", depending on their mass and level of ionization . On impact in the cups, the ions set up a very weak current that can be measured to determine the rate of impacts and the relative concentrations of different atoms in the beams . </P>

How do you calculate the age of a rock using radiometric dating