Rock on 10

You start with 400 parent atoms of a particular radioactive type, which decays in a single step to give a stable offspring, and you start with none of those stable offspring. You wait just long enough for two half lives to pass. You should expect to have how many offspring atoms (on average)(remember that the number of parents and the number of offspring add up to 400, so if you have 10 parents, you have 390 offspring because 10 and 390 add up to 400, and if you have 20 parents you have 380 offspring, and so on):

100 After one half-life, you've gone from 400 parents to 200, and 200 offspring have been made. In the second half-life, you go from 200 to 100 parents, and that makes another 100 offspring. Adding the additional 100 to the 200 from the previous half-life gives 300 offspring. (Typical studies of radioactive decay use many more atoms, to avoid statistical fluctuations, but the question says "on average", so we asked you about 400 rather than 400,000,000,000,000 to make the math easier.)

What is indicated by the yellow lines in the image above?

A great unconformity, with sedimentary rocks above resting on older sedimentary rocks below. John Wesley Powell, of the United States Geological Survey, and the leader of the first boat trip through the Grand Canyon, called the feature marked by the yellow lines "The Great Unconformity". It separates horizontal Paleozoic sedimentary rocks, above, from inclined Precambrian sedimentary rocks, below.

The age of the Earth can be estimated in many ways. Which statement below is most accurate (remember that uniformitarian calculations involve looking at the thickness and type of sedimentary rocks, and similar things, but do NOT include radiometric dating or counting of annual layers)?

Annual-layer counting shows that the Earth is more than about 100 thousand years old, uniformitarian calculations show that the Earth is more than about 100 million years old, and radiometric techniques tell us how old the Earth is.

The diagram above shows a geologic cross-section of some rocks, such as you might see in a cliff. The tree is growing on top of the modern surface. Rock layers A, B, C, D, E, and F are sedimentary; E contains mud cracks and fossil footprints as shown. G is igneous rock that hardened from hot, melted rock. H, I and J are faults, and K and L are unconformities. Sedimentary rocks are right-side-up unless there is some indication given to show something else. Referring to the rocks you see here ......Which is the oldest sedimentary rock layer?

C The package of sediments C, D, E, and F is upside-down, as shown by the footprints and mud cracks, so C is the oldest one.

Which is the oldest sedimentary rock layer:

C The package of sediments C, D, E, and F is upside-down, as shown by the footprints and mud cracks, so C is the oldest one.

Which is older:

Fault I. Fault I is cut by fault J, so is older than J. Fault J is cut by unconformity K so is older than K. Unconformity K is cut by intrusion G so is older than G, and intrusion G is cut by fault H so is older than H. Hence, fault I is the oldest on this list.

Which correctly gives the order of the faults, from oldest (first) to youngest (last):

I, J, H I is cut by J, so I is older than J. And with reference to K, both I and J can be shown to be older than H.

Which is accurate about the history of the Grand Canyon:

In the deepest part of the canyon, the river cuts through rocks formed by metamorphism of older sedimentary rocks in the heart of a mountain range. The Colorado River is cutting through the metamorphic rocks from the heart of an old mountain range. The sedimentary rocks above are right-side up, and the Kaibab Limestone slants down to the north beneath the rocks of Zion, which are older than the rocks of Bryce, among others. Many unconformities exist in the walls of the Canyon, including the one below the Precambrian sediments and the one above those sediments. The idea of the river narrowing over time was the hypothesis that an interested tourist presented to one of the professors and a ranger at the Canyon a few years ago. When the professor asked whether the tourist would want to go out on a narrow point with a jackhammer, the tourist said no, because the rocks might fall off and slide down into the Canyon. When the professor pointed out the many places that rocks had fallen off and slid down, the quick-witted tourist figured out that the Canyon has been widened by such rockfalls as the river has cut downward.

Geological evidence based on several radiometric techniques has provided a scientifically well-accepted age for the Earth. Represent that age of the Earth as the 100-yard length of a football field, and any time interval can be represented as some distance on the field. (So something that lasted one-tenth of the age of the Earth would be ten yards, and something that lasted one-half of the age of the Earth would be fifty yards.) On this scale, how long have you personally been alive?

Much less than the thickness of a sheet of paper. If the 4.6 billion years of Earth history are 100 yards, then the few thousand years of written history are just one-millionth of that history, just over the thickness of a sheet of paper. And your small piece of written history must be only a small fraction of a sheet of paper, roughly 1/200th or so.

The above photograph was taken in the Grand Canyon, and shows a cliff that is approximately 30 feet high. What are the rocks in the cliff?

Precambrian metamorphic rocks with some igneous rocks intruded; the folding was caused by mountain-building processes when the rocks were very hot deep in a mountain range. This is the Vishnu Schist and Zoroaster Granite, rocks from the heart of a mountain range. The river is just barely out of the picture to the bottom.

In age dating, geologists use:

Radiometric techniques and layer-counting for absolute dating of events that happened in the last 100,000 years, and other radiometric techniques for absolute dating of much older events. If you want an absolute date (number of years) rather than older/younger, you can count layers for young things, or use radiometric techniques for young things or for old ones.

What is accurate about the scientific results learned by counting tree rings and other annual layers?

Records in tree rings, lakes and ice all reach beyond 12,000 years, and some of them reach beyond 40,000 years. There is a continuous record of overlapping tree rings from north Germany with 12,429 years in trees (and that was published a few years ago). The longest lake-sediment record of annual layers is over 40,000 years, and there are over 100,000 years in the longest ice-core record that preserves annual layers. And, various lake, tree and ice records agree on the history of volcanoes, climate changes, etc.

The two pictures above, I and II, show fossils inrocks from the Grand Canyon. Each is "typical"; the rocks near sample Icontain fossils similar to those shown in sample I, and the rocks nearsample II contain fossils similar to those shown in sample II. It is likely that:

Sample I is from high in the cliffs of the Grand Canyon, and sample II is from much lower, near the river. Sample I is a wonderful shell hash, or coquina, from the Supai Rocks well up the side of the Canyon, and contains shells from a great diversity of different creatures. Sample II includes algal-mat deposits (stromatolites) from the Precambrian Chuar Group of the Grand Canyon Supergroup, deep in the Canyon near the river, from a time when biology was not a whole lot more diverse than algal mats. Lake Winna-Bango featured in the gripping Dr. Suess tale of Thidwick, the Big-Hearted Moose, but is not pictured here.

One practical radioactive system used to date lava flows involves:

The solid potassium-40, which decays to the gas argon-40. Potassium-40 is common in solid minerals, and decays to produce the gas argon-40. And despite his great contributions to humanity, no one has named an isotope after moose moss (the favorite food of Thidwick, for you Dr. Suess fans).

Which is younger:

The tree. The tree is growing on intrusion G, which can be shown to be younger than all of the others.

The picture above shows a region of hard rock about six inches across from the Grand Canyon. The shape and polish of the rock are interesting. It is likely that the rock:

Was scratched and polished by silt-laden river water, during carving of the Canyon by the Colorado River. The Canyon was carved by the Colorado River. Glaciers have not been there, and while wind, faults and mule hooves all can change the appearance of rocks, none makes something like this river-polished rock, as you saw in the class materials including in one of the Grand Canyon slide shows.

You are dating a lava flow by the potassium-argon system. However, the offspring in this system are leaking out of the minerals. Which is accurate?

You will think that the lava flow is younger than it really is, but you will be able to detect the error by comparing concentrations of offspring from the edges and centers of grains. Argon-40 leakage will make the lava flow appear young even if the flow is old; however, the edges of grains will lose more argon-40 than will the centers, pointing to the source of the error.