A note for NTSE students

I have started a new blog exclusively for the NTSE students. Click at the following link to read the contents:
http://ntsephysics.blogspot.com/ 

Gears in a watch

In a clock the gear system is connected to the seconds hand, minutes hand and the hour hand. The gear wheel attached to the seconds arm has 120 teeth and is connected to a pendulum having a period of half a second. This means that two teeth are able to advance in 1 second the entire revolution of the seconds hand takes 60 seconds or one minute.This gear is made to  drive another gear train with a ratio of 1:60 and  the minute hand is attached to the last gear in that train. A final train with a ratio of 1:12 is attached to the hour hand.

Here's the link where you can see this in action:

http://electronics.howstuffworks.com/gadgets/clocks-watches/clock3.htm

Regelation

The phenomenon due to which ice melts to water at a temperature below 0o C melts to water on the application of external pressure and refreezing of water formed into ice on the release of pressure is called regelation.

Examples of Regelation :

1. When two pieces of ice are pressed together they form a single piece on releasing pressure. This happens because pressure lowers the melting point and makes the ice melt at the surface of contact. On releasing pressure the melting point is raised once again and and the water formed refreezes once again.

2. Glaciers move slowly in the downward direction at sub zero ( below 0o C)  temperature due to regelation. Ice present at the base of the glacier experiences tremendous pressure due to the weight of the glacier. This causes the ice to melt at the base of the glacier. As the water formed flows out from the base of the glacier, it does not experience any pressure and refreezes to form ice once again.

Uranium-Lead Dating

When rocks are formed, small amounts of radioactive elements usually get included. As time passes, the "parent" radioactive element (which is uranium in this case) changes at a regular rate into non-radioactive "daughter" element (which is uranium in this case). Thus, the older a rock is, the larger the number of daughter atoms and the smaller the number of parent atoms are found in the rock. In this case as the rock ages, more and more of the uranium  changes into lead.The of the rock in years can be found by measuring the rate at which a uranium decays and then measuring the ratio of uranium to lead in the rock.

Carbon-14 dating

Carbon-14  is a radioactive isotope of carbon with a nucleus containing 6 protons and 8 neutrons. Its presence in organic materials is the basis of the radiocarbon dating method to determine the age of fossils. Carbon has three naturally occurring isotopes. Both C-12 and C-13 are stable, but C-14 decays by very weak beta decay to nitrogen-14 with a half-life of approximately 5,730 years.

Cosmic ray protons blast nuclei in the upper atmosphere, producing neutrons which in turn bombard nitrogen of the atmosphere to  produce the radioactive isotope carbon-14 according to the following reaction:
0n1 + 7N14→ 6C14 + 1H1

The radioactive carbon-14 combines with oxygen to form carbon dioxide.

Now plants take in  CO2 for photosynthesis and so (while they are living) they have the same ratio of carbon 14 in them as the atmosphere. Animals, including humans, consume plants and thus they also tend to have the same ratio of carbon 14 to carbon 12 atoms. This equilibrium persists in living organisms as long as they continue living, but when they die the intake of carbon 14 stops.

Carbon 14  decays into nitrogen-14 through beta decay according to the following reaction:

6C14    →  7N14   +   -1e0

Presuming the rate of production of carbon-14 to be constant, the ratio of C-14 and C-12 in a fossil can help us to determine the age of the fossil.