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Chapter 9: Q15CQ (page 403)

:In a certain design of helium-neon laser, the chamber containing these gases has a perfect mirror at one end. as usual, but only a window at the other, Beyond the window, is a region of free air space and then the second mirror, which is partially reflecting, allowing the beam to exit. The resonant cavity between the mirrors thus has a region free of the helium-neon gas-the "lasing material"-in which you can insert something. If you insert a sheet of clear plastic at any orientation in this region between the mirrors, the laser beam disappears. If the same sheet is placed in the beam outside the partially reflecting mirror, the beam passes through it, regardless of the orientation. Why?

Short Answer

Expert verified

Angular quantum number, l: represents the shape of the orbital of Hydrogen

Magnetic quantum number, ml: represents the energy levels in sub shell.

Step by step solution

01

The quantum mechanical model

The Quantum-mechanical model of an atom provides with a few quantum numbers which helps to determine the exact location of electron in an atom.

The first quantum number is the Principal Quantum number which is represented byn, it represents the shell number to which an electron belongs.

For a one-dimensional particle in a box, the n represents the shell to which electron belongs. The value ofn may be 1,2,3___n

02

The meaning of n for a hydrogen atom.

In one electron atom like Hydrogen, Principal Quantum number holds a great significance. It can specify the radial distributions of the wave function and the energy values of the atom with different values It also specifies the radial dependence of the radial wave function.

03

The meaning of I  and ml for Hydrogen-atom.

Just like Principal quantum numbern,there are three more quantum numbers, out of which two are- angular quantum number,land the magnetic quantum number,ml.

In the Hydrogen atom:

Angular quantum number, l: represents the shape of the orbital of Hydrogen

Magnetic quantum number, ml: represents the energy levels in sub shell.

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Most popular questions from this chapter

According to Wien's law, the wavelength位maxat which the thermal emission of electromagnetic energy from a body of temperatureTis maximum obeys位maxT=2.898脳10鈭�3m鈰�K.Show that this law follows from equation (9-47). To do this. Usef=c/位to expressin terms of位rather than f, then obtain an expression that, when solved, would yield the wavelength at which this function is maximum. The transcendental equation cannot be solved exactly, so it is enough to show that位=(2.898脳10鈭�3m鈰�K)/T solves it to a reasonable degree of precision.

Consider a simple thermodynamic system in which particles can occupy only two states: a lower state, whose energy we define as 0 , and an upper state, energyEu鈭�

(a) Cany out the sum (with only two states, integration is certainly not valid) giving the average particle energy E. and plot your result as a function of temperature.

(b) Explain qualitatively why it should behave as it does,

(c) This system can be used as a model of paramagnetic, where individual atoms' magnetic moments can either be aligned or anti aligned with an external magnetic field, giving a low or high energy, respectively. Describe how the average alignment or antialignment depends on temperature. Does it make sense'?

(a) From equation (9.34) and the Fermi-Dirac distribution given in Exercise 53, obtain an expression for EF(T), the Fermi temperature for a collection of fermion oscillators, (b) Show that EFo=蔚. (c) Plot EF(T)versuskBT蔚from 0tokBT6=1.5. (d) By what percent does the Fermi energy drop from its maximum T=0value when kBTrises to 25%of蔚?

The diagram shows two systems that may exchange both thermal and mechanical energy via a movable, heat-conducting partition. Because both Eand Vmay change. We consider the entropy of each system to be a function of both:S(E,V). Considering the exchange of thermal energy only, we argued in Section 9.2 that was reasonable to define1Tas未S未E. In the more general case, PTis also defined as something.

a) Why should pressure come into play, and to what mightPTbe equated.

b) Given this relationship, show thatdS=dQT(Remember the first law of thermodynamics.)

Suppose we have a system of identical particles moving in just one dimension and for which the energy quantization relationship isE=bn2/3, wherebis a constant andan integer quantum number. Discuss whether the density of states should be independent ofE, an increasing function ofE, or a decreasing function ofE.
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