Consider the wavefunction for a particle in a one-dimensional box when the level is n = 6. Calculate the total probability of finding the particle between x = 0 and x = L/12? Provide your answer to three significant figures.

A relativistic electron has a de Broglie wavelength of 1.25 pm1.25 pm (1 pm=10−12 m).(1 pm=10−12 m). Determine its velocity, expressed as a fraction of the speed of light ?.

Can you please help me with part C and D?

In a ground state atom of S how many electrons total will have the quantum number l=0?

1. • Make a chart showing all the possible sets of quantum num- bers / and m, for the states of the electron in the hydrogen atom when n = 3. How many combinations are there?

Consider a particle trapped in a iD box with zero potential energy with walls at x = 0 and x = L. The general wavefunction solutions for this problem with quantum number, n, are: yn(x) = The corresponding energy (level) for each wavefunction solution is: n?h? En 8ml? a) Is the particle always uniformly distributed throughout the box? Explain your answer. b) Consider the molecules: CH2=CH-CH=CH-CH=CH-CH=CH-CH=CH2. Follow from Ex 4.7 in the textbook, let's assume that the 1o electrons that make up the double bonds can exist everywhere along the carbon chains. The electrons can then be considered as particles in a box; the ends of the molecule correspond to the boundaries of the box with a finite or zero potential energy inside. In this "molecular box", 2 electrons can occupy an energy level. What are quantum states that the electrons from this molecule can occupy in the ground state? What's the smallest frequency of light that can excite the electron? Briefly explain why. Note that the…