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a/ What is its wavelength? What is the color of this light?
b/ What is the smallest possible uncertainty in energy (in eV) of the photon?
2)Find the width L of a one-dimensional box that would correspond to the absolute value of the ground state of a hydrogen atom. What is your observation?
a/ A particle of mass m is contained in a one-dimensional box of width a. The potential energy U(x) is infinite at the walls of the box (x = 0 and x = a) and zero in between (0 < x < a).
Show that the solutions have the form: U(x)=Csin(n.pi.x/a) . Find the constant C.
b/ For the case n = 3, find the probability that the particle will be located in the region a/3 <x< 2a/3
c/ Sketch the wave-functions and the corresponding probability density distributions for the cases n = 1, 2 and 3.
2)We have the energy level for hydrogen atom: .En=-13.6eV/n^2
a/ For high principle quantum number (n) for hydrogen atom show that the spacing between the neighboring energy levels is proportional to .1/n^3
b/ In which transition of hydrogen atom is the wavelength of 486.1 nm produced? To which series does it belong?
Explain what happens when a body is raised to a height from the surface of earth and then given a horizontal velocity v such that:
i) 0 < v < 8.0 km/s
ii) v = 8.0 km/s
iii) 8.0 < v < 11.2 km/s
iv) v = 11.2 km/s