A gas can be too cold to absorb Balmer series lines. Is this also true for the Panchen series? (See Figure 7.5.) for the Lyman series? Explain.
It is true for Paschen series but not true for Lyman series.
Paschen series is a sequence of emission or absorption lines along the infrared part of hydrogen atom. It is caused by the movement of electron between 3rd energy level and the higher levels
The Lyman series is a series of ultraviolet spectrum lines of atomic hydrogen between 122 and 91 nanometres.
A gas can be too cold to absorb wavelengths of light belonging to the Balmer series because the transitions involve the electron being initially in the n = 2 excited state and absorbing a photon to change to a higher excited state, and the Balmer series transitions will not be observed.
The Paschen series results from transitions in which the atom is initially in its ground state. Because the ground state is populated no matter how cold the gas is, so it can always absorb wavelengths belonging to the Paschen series.
Absorption lines, in the Lyman series result from transitions in which the atom is initially in the n = 3 excited state and here too if the gas is too cold the n = 3 state is not populated and the absorption transition in the Lyman series cannot occur.
Thus, it is true for Paschen series but not true for Lyman series.
Exercise 81 obtained formulas for hydrogen like atoms in which the nucleus is not assumed infinite, as in the chapter, but is of mass , while is the mass of the orbiting negative charge. (a) What percentage error is introduced in the hydrogen ground-state energy by assuming that the proton is of infinite mass? (b) Deuterium is a form of hydrogen in which a neutron joins the proton in the nucleus, making the nucleus twice as massive. Taking nuclear mass into account, by what percent do the ground-state energies of hydrogen and deuterium differ?
Residents of flatworld-a two-dimensional world far, far away-have it easy. Although quantum mechanics of course applies in their world, the equations they must solve to understand atomic energy levels involve only two dimensions. In particular, the Schrodinger equation for the one-electron flatrogen atom is
(a) Separate variables by trying a solution of the form , then dividing by . Show that the equation can be written
Here, is the separation constant.
(b) To be physically acceptable, must be continuous, which, since it involves rotation about an axis, means that it must be periodic. What must be the sign of C ?
(c) Show that a complex exponential is an acceptable solution for .
(d) Imposing the periodicity condition find allowed values of .
(e) What property is quantized according of C .
(f) Obtain the radial equation.
(g) Given that , show that a function of the form is a solution but only if C certain one of it, allowed values.
(h) Determine the value of a , and thus find the ground-state energy and wave function of flatrogen atom.
A spherical infinite well has potential energy
Since this is a central force, we may use the Schrodinger equation in the form (7-30)-that is, just before the specific hydrogen atom potential energy is inserted. Show that the following is a solution
Now apply the appropriate boundary conditions. and in so doing, find the allowed angular momenta and energies for solutions of this form.
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