Scientists say that it is hard to track how monarch butterflies migrate
It totally depends on what kind of wave you're talking about.
-- a sound wave from a trumpet or clarinet playing a concert-A pitch is about 78 centimeters long ... about 2 and 1/2 feet. This is bigger than atoms.
-- a radio wave from an AM station broadcasting on 550 KHz, at the bottom of your radio dial, is about 166 feet long ... maybe comparable to the height of a 10-to-15-story building. This is bigger than atoms.
-- a radio wave heating the leftover meatloaf inside your "microwave" oven is about 4.8 inches long ... maybe comparable to the length of your middle finger. this is bigger than atoms.
-- a deep rich cherry red light wave ... the longest one your eye can see ... is around 750 nanometers long. About 34,000 of them all lined up will cover an inch. These are pretty small, but still bigger than atoms.
-- the shortest wave that would be called an "X-ray" is 0.01 nanometer long. You'd have to line up 2.5 billion of <u>those</u> babies to cover an inch. Hold on to these for a second ... there's one more kind of wave to mention.
-- This brings us to "gamma rays" ... our name for the shortest of all electromagnetic waves. To be a gamma ray, it has to be shorter than 0.01 nanometer.
Talking very very very very roughly, atoms range in size from about 0.025 nanometers to about 0.26 nanometers.
The short end of the X-rays, and on down through the gamma rays, are in this neighborhood.
Well, the unit of measurement would be the Hertz (after Heinrich H) Hz. But, that doesn't by itself, cover the harmonic content of pitch. Does middle C on a piano sound the same as it does on a trumpet or a violin ? Answer is prob not. Reason is that apart from C (about 256Hz) there are harmonics. The harmonics are also in Hz, and spectrum analysis is one way of seeing the "signatures" of different sound sources of the same "pitch" but different sources. Tuning forks sort of work sort of similarly sort of ...
Answer:
The probability of finding the proton at the central 2% of the well is almost exactly 4%
Explanation:
If we solve Schrödinger's equation for the infinite square well, we find that its eigenfunctions are sinusoidal functions, in particular, the ground state is a sinusoidal function for which only half a cycle fits inside the well.
let be the well's length, the boundary conditions for the wavefunction are:
And Schrödinger's equation is:
The solution to this equation are sines and cosines, but the boundary conditions only allow for sine waves. As we pointed out, the ground state is the sine wave with the largest wavelength possible (that is, with the smallest energy).
here the leading constant is just there to normalise the wavefunction.
Now, if we know the wavefunction, we can know what the probability density function is, it is:
So in our case:
And to find the probability of finding the particle in a strip at the centre of the well of width 2% of L we only have to integrate:
If we do a substitution:
We get the integral:
This integral can be computed analytically, and it's numerical value is .0399868, that is, almost a 4% probability.