What are isotopes? In what ways are they similar? In what ways do they differ?
Isotopes are the same element with different mass numbers. C-14 and C-13 are isotopes of each other. They are both the element Carbon, however they have different mass numbers; 14 and 13. Both of these samples have 6 protons. All elements of the same element MUST contain the same number of protons, as identified by the atomic number of the element, represented on the Periodic Table of Elements. Since these samples are not ions (charged), they must also have the same number of electrons. In an atom (an uncharged sample) the number of protons and electrons must be equal. Since the mass numbers of these two samples are different, this means that the number of neutrons must be different. Mass number of a sample is determined by adding together the number of protons and neutrons. Let's look at these two samples. We have already decided that the number of protons in C-14 and C-13 must be equal. They both have 6 protons because the atomic number of Carbon is 6. Carbon-14, therefore, has 8 neurons. How did I get this? We already decided that the mass number is equal to the number of protons plus the number of neutrons. We know the mass number because it is given in the sample's name. Carbon-14 indicates that we have a sample of Carbon with a mass number of 14. Therefore, 14-6=8. (14 being the mass # - 6, which is the number of protons = 8 which is the number of neutrons. Now let's do the same thing with C-13. Carbon-13 must have a mass number of 13. Carbon-13 has 6 protons because again it has an atomic # of 6. Let's do the same math as before. 13-6 = 7. Therefore the sample of carbon-13 has 7 neutrons. Recap: Isotopes have the same: 1. # of protons (they are samples of the same element and have the same atomic # which means they have the same amount of protons. 2. # of electrons (since they are atoms and not ions, they must have the same number of protons and electrons.) Isotopes have different: 1. Mass numbers and therefore different number of neutrons. (mass number = # of protons + # of neutrons)
Vaccines are a subject of great debate amongst parents and doctors. What exactly are vaccines? How do vaccines help us, not only as individuals, but also as a population?
The purpose of vaccines is to prevent certain communicable and sometimes fatal diseases. When you receive a vaccine, you are receiving a dead or weakened version of the pathogen; or the organism that causes disease. You may be asking, "how would a dead version of this pathogen help me?" Well the answer is pretty simple. All cells have antigens. Antigens are simply proteins located on the outside of the cell that identify what the cell is. Think of it as a name tag. The cells in your body all have the same antigens so that your immune system can identify these cells as "good" cells and will not attack them. The pathogen also contains antigens. Once this cell gets into your body, your immune system, specifically your white blood cells will recognize a "foreign" antigen. This will cause an immune response. Your body will begin to fight off the pathogen (even though it is dead). Antibodies are made in response to the pathogen. These antibodies will stay in your body forever. Let's say for example, that you received the vaccine for chicken pox. Your body will create antibodies to the chicken pox virus, without you actually getting the chicken pox. Why is this important? If you ever come in contact with someone who has the chicken pox and are reinfected, your body will call up these antibodies and fight it off before you even experience symptoms. As you can see, vaccines can help an individual so that they do not become infected with communicable and possibly fatal diseases. However, how does being vaccinated help us as a community? There are many people that cannot receive vaccines because of a different health issue. They are, therefore, at great risk of contracting these preventable diseases. If people around them are vaccinated, it can drastically prevent the spread of disease to those who cannot be vaccinated.
What is the basic method used to solve a parabolic trajectory question?
There are several steps to this process. The first step is that you must split up the motion of the trajectory into an x (horizontal) motion and a y (vertical motion). Think about when you "lob" a ball to your friend. The ball has both height (y) and distance (x). From here you would create a chart to show acceleration, initial velocity, final velocity, and distances in both the x and y directions. Once you have completed your chart, you can refer to your kinetics equations and decide which formula you use to determine the missing variables (this will differ depending on the variables given in the problem to be solved).