Answer:
P = 1/8
Explanation:
The wave function of a particle in a one-dimensional box is given by:
Hence, the probability of finding the particle in the one-dimensional box is:
Evaluating the above integral from x₁ = 0 to x₂ = L/8 and solving it, we have:
![P = \frac{2}{L} [\frac{L}{16} (1 - 4\frac{sin(\frac{n \pi}{4})}{n \pi})]](https://tex.z-dn.net/?f=%20P%20%3D%20%5Cfrac%7B2%7D%7BL%7D%20%5B%5Cfrac%7BL%7D%7B16%7D%20%281%20-%204%5Cfrac%7Bsin%28%5Cfrac%7Bn%20%5Cpi%7D%7B4%7D%29%7D%7Bn%20%5Cpi%7D%29%5D%20)
Solving for n=4:
I hope it helps you!
Answer:
we know that gas molecules move fast by hitting the container and they never meet,so if we have one single gas molecule then it will move slower . This is because it is alone in an empty container so until it hits the container to change it's movements it will make the process slower.
Read the explanation below to have a better idea based on the kinetic molecular theory.
Explanation:
Hello in this question we have a container and in it is a single gas molecule. So there is our gas molecule and in fact right there that violates the kinetic molecular theory. Because the kinetic molecular theory thinks of these particles as being dimension less points. Because there is so much space between particles. The particles themselves have such an insignificant volume as they can be thought of as dimension lys points. Okay. But anyway this particle is in rapid motion and this motion is essentially random. So it's moving and it will eventually hit the wall of its container. It's moving rapidly so it's going to hit it pretty quickly and when it hits the wall of that container Yeah, it is going to bounce off when it does that. It's a totally elastic collision. So that means there will be no energy transfer, no energy loss, no energy gained. It will just serve to change the direction of the particle. So when it hits the wall it's going to bounce back off the wall and continue in a straight line until it hits another wall and then it will bounce off that wall and it will continue moving in this motion in this motion its speed is related to the amount of energy it has and therefore its temperature. So if we add heat, it will move faster. If we remove heat or cool it down, it will move slower. So when we remove heat, it will move slower. The kinetic molecular theory says it will be constantly moving As long as it is above absolute zero. It's only at absolute zero or 0 Kelvin, where would stop moving. Okay, so all these things describe its motion. It's in rapid random motion in a straight line until it hits the wall of its container. Then it will rebound without a transfer of any energy. It will be totally elastic collision. If we were to heat it up, it would move faster. If we were to cool it down, it would move more slowly, we would have to cool it all the way down to absolute zero before it would stop moving. Right, so all of these things describe its motion. In terms of that kinetic molecular theory,
I believe the answer you're looking for is, D. The motion of atoms and molecules.
