## Absolute Age Dating How We Know When Dinosaurs Lived

When geologists confidently say that dinosaurs as a group lived for, at a minimum, 165 million years, or 165 Ma (Latin translation of mega annus), they are referring to the considerable factual evidence supporting the vast amounts of time associated with the age of the Earth. That the Earth is about 4.6 billion years old is known through radiometric age dating, a method used to calculate absolute ages of rocks or other materials using radioactive elements. Radioactive elements have known natural decay constants, which are unvarying rates of radioactive decay over time. Radioactive elements are unstable elements that give off matter and energy in a way that results in their eventual change of one element (the parent element) to another (daughter element). Steps in between the parent and final stable daughter element are represented by a number of elements and constitute a decay sequence. The general equation for radioactive decay is represented by the formula:

where N is the number of atoms present now, N0 is the original number of atoms from the radioactive element, e is a constant (about 2.718), X is the decay constant, and t is time. With some algebraic re-arranging, the formula is changed to solve for t, which gives the age of the rock.

Age dates derived from such methods are also cross-checked against the many facts provided by relative age dating (Fig. 4.5). The checking and rechecking of radiometric

FIGURE 4.5 Igneous rock cross-cutting sedimentary rock (Pen Formation) in Big Bend National Park, Texas. The sedimentary rock has fossils indicating that it is Late Cretaceous, about 70 Ma. The cross-cutting igneous rock should be younger, and it is. Radiometric dates derived from it and related rocks in the region indicate that they were formed in the Tertiary Period. English professor for scale.

FIGURE 4.5 Igneous rock cross-cutting sedimentary rock (Pen Formation) in Big Bend National Park, Texas. The sedimentary rock has fossils indicating that it is Late Cretaceous, about 70 Ma. The cross-cutting igneous rock should be younger, and it is. Radiometric dates derived from it and related rocks in the region indicate that they were formed in the Tertiary Period. English professor for scale.

age dates through independently verifiable and repeatable tests, as well as the common applications of quantum physics, makes radiometric age dating scientifically certain. Likewise, decay constants of radioactive elements provide us with extremely accurate means of measuring the ages of phenomena that occurred long before human history, such as dinosaurs and their associated rocks. Rates of decay have never been observed to change in any significant way under a wide variety of laboratory conditions; hence these rates are as factually-based as the effects of gravity. For an analogy, speculating that a radioactive element may have had a random or otherwise variable decay rate is akin to saying that apples may have fallen up rather than down from trees at random times in the past.

First, some backtracking to define a few basic terms is necessary. An element is a substance composed of atoms that contain the same number of protons; this number of protons defines the atomic number of an element. Protons are positively-charged particles with a standard atomic mass of 1.0, the same mass for neutrally charged neutrons. Both protons and neutrons are in the nucleus, the center of the atom. Negatively charged electrons, with masses about 1/1800 of protons and neutrons, orbit the nucleus. Atomic mass is calculated simply by adding the number of protons and neutrons in an atom, ignoring the negligible mass provided by electrons. For example, some atoms of carbon have 6 protons and 6 neutrons, thus it has an atomic number of 6 and an atomic mass of 12 (written also as 12C). Atoms with the same atomic number are all the same element; 12C, 13C, and 14C have different masses as they have more or less neutrons because they have the same atomic number, and they are isotopes of an element. Remember that the number of protons stays the same, otherwise it becomes a different element.

A radioactive element that is actively emitting energy may be transmitting it through moving particles. Particles that are commonly emitted by radioactive elements are alpha particles, which are two protons and two neutrons (equivalent to the nucleus of a helium atom, which has an atomic mass of 4), and beta particles, which are high-speed electrons. Appropriately enough, radiation that consists of alpha particles is called alpha radiation, and radiation that consists of beta particles is beta radiation. These types of radiation result from decay of a radioactive element because when atoms lose particles they change into different elements. For example, here is part of the decay sequence for uranium-238 (238U), which has an atomic number of 92 (hence having 146 neutrons):

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