Answer:
![[\psi]= [Length^{-3/2}]](https://tex.z-dn.net/?f=%5B%5Cpsi%5D%3D%20%5BLength%5E%7B-3%2F2%7D%5D)
- This means that the integral of the square modulus over the space is dimensionless.
Explanation:
We know that the square modulus of the wavefunction integrated over a volume gives us the probability of finding the particle in that volume. So the result of the integral
must be dimensionless, as represents a probability.
As the differentials has units of length
![[dx]=[dy]=[dz]=[Length]](https://tex.z-dn.net/?f=%5Bdx%5D%3D%5Bdy%5D%3D%5Bdz%5D%3D%5BLength%5D)
for the integral to be dimensionless, the units of the square modulus of the wavefunction has to be:
![[\psi]^2 = [Length^{-3}]](https://tex.z-dn.net/?f=%5B%5Cpsi%5D%5E2%20%3D%20%5BLength%5E%7B-3%7D%5D)
taking the square root this gives us :
![[\psi] = [Length^{-3/2}]](https://tex.z-dn.net/?f=%5B%5Cpsi%5D%20%3D%20%5BLength%5E%7B-3%2F2%7D%5D)
<span>Transformed into potential energy</span>
Solution: (i) Density (ii) thermal
Liquids at lower temperatures have greater density when compared to liquids at higher temperatures.This is because, at higher temperatures, molecules have greater kinetic energy and hence they are spaced farther apart, when compared to molecules at lower temperatures. Thus, the colder layers of liquids are heavier than the warmer layers, which causes then to move down due to gravity. For the same reason, the hotter layers move upwards through the liquid.
When a liquid is heated, the molecules closest to the heat source have greater energy, their density becomes less and they move upwards. The colder layers sink downwards. The layers of the liquid which were cold initially, get heated and they travel upwards. As the process repeats, convection currents are set up in the liquid.
These currents transfer the thermal energy derived from the source throughout the liquid. The process stops when the entire liquid is at the same temperature.
Thus, convection currents occur in liquids due to temperature and <u>density</u> differences. Convection currents transfer <u>thermal</u> energy throughout a fluid.
