: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

For a particle in a one-dimensional (ID) box, Enis proportional to a single quantum number n. Let us simplify things by ignoring the proportionality factor: En=n2 . For a 3D box, Enx,ny,nz=nx2+ny2+nz2, and the 2D box is fairly obvious.

(a) The table shows a start on accounting for allowed states. Complete the table, stopping after the 10th state (state, not energy) for all three cases.

(b) Find the number of states per energy difference for the first five states and the last five states for all three cases. For instance, for the first five in the ID case, it is 5 states per energy difference of 24, or5/24 .

(c) Overlooking the obviously crude aspects of this accounting, does the "density of states" seem to increase with energy, decrease with energy, or stay about the same?

(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=ε. (c) Plot EF(T)versuskBTεfrom 0tokBT6=1.5. (d) By what percent does the Fermi energy drop from its maximum T=0value when kBTrises to 25%ofε?

Consider the two-sided room, (a) Which is more likely to have an imbalance of five particles (i.e. Nk=12N+S,S): a room withN=20or a room withrole="math" localid="1658330090284" N=60? (Note: The total number of ways of distributing particles. the sum ofWNhNfrom 0 toN, is2N.) (b) Which is more likely to have an imbalance of5%(i.e. NR=12N+0.05N,)? (c) An average-size room is quite likely to have a trillion mote air molecules on one side than on the other, what may we say that precisely half will be on each side?

In a large system of distinguishable harmonic oscillator how high does the temperature have to be for the probable number of particles occupying the ground state to be less than 1 ?

The Stirling approximation.J!2πJJ+1/2e-J, is very handy when dealing with numbers larger than about100 . Consider the following ratio: the number of ways Nparticles can be evenly divided between two halves of a room to the number of ways they can be divided with60%on the right and40%on the left.

(a) Show, using the Stirling approximation, that the ratio is approximately4046065Nfor largeN.

(b) Explain how this fits with the claim that average behaviours become more predictable in large systems.

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