Describe the quantum mechanical model of the atom and several observations which support this model.

This means that we shouldn't imagine electrons as single objects going around the atom. Instead, all we know is the probability of finding an electron at a particular location. What we end up with is something called an electron cloud. An electron cloud is an area of space in which an electron is likely to be found. It's like a 3-D graph showing the probability of finding the electron at each location in space. Quantum mechanics also tells us that a particle has certain numbers (called quantum numbers) that represent its properties. Just like how materials can be hard or soft, shiny or dull, particles have numbers to describe the properties. These include a particle's orbital quantum numbers, magnetic quantum number, and its spin. No two electrons in an atom can have exactly the same quantum numbers. Orbital quantum numbers tell you what energy level the electron is in. In the Bohr model, this represents how high the orbit is above the nucleus; higher orbits have more energy. The first orbit is n=1, the second is n=2, and so on. The magnetic quantum number is just a number that represents which direction the electron is pointing. The other important quantum mechanical property, called spin, is related to the fact that electrons come in pairs. In each pair, one electron spins one way (with a spin of one half), and the other electron spins the other way (with a spin of negative one half). Two electrons with the same spin cannot exist as a pair. This might seem kind of random, but it has effects in terms of how magnetic material is. Materials that have unpaired electrons are more likely to be magnetic

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

blue light is scattered in different directions by the tiny molecules of air. blue is scattered more than other colours because it has a shorter distance to travel which results in smaller waves. this is why we see a blue sky most of the time.