: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

Example 9.2 obtains a ratio of the number of particles expected in the n = 2state lo that in the ground state. Rather than the n = 2state, consider arbitrary n.

(a) Show that the ratio is numberofenergyEnnumberofenergyE1=n2e-13.6cV(1-n-2)/kBT

Note that hydrogen atom energies are En=-13.6eV/st2.

(b) What is the limit of this ratio as n becomes very large? Can it exceed 1? If so, under what condition(s)?

(c) In Example 9.2. we found that even at the temperature of the Sun's surface(~6000K), the ratio for n = 2 is only 10-8 . For what value of nwould the ratio be 0.01?

(d) Is it realistic that the number of atoms with high n could be greater than the number with low n ?

Obtain equation (9- 15) from (9-14). Make use or the following sums, correct when |x|<1 :

n=0xn=11-xn=0nxn=x(1-x)2

A particle subject to a planet's gravitational pull has a total mechanical energy given by Emechanical=12mv2-GMmr, whereis the particle's mass.M the planet's mass, and Gthe gravitational constant6.67×10-11N·m3/kg2. It may escape if its energy is zero that is, if its positive KE is equal in magnitude to the negative PE holding if to the surface. Suppose the particle is a gas molecule in an atmosphere.

(a) Temperatures in Earth's atmosphere may reach 1000K. Referring to the values obtained in Exercise 45 and given that REarth=6.37×106mand MEarth=5.98×1024kg. should Earth be able to "hold on" to hydrogen (1g/mol)? 10 nitrogens (28g/mol)? (Note: An upper limit on the number of molecules in Earth's atmosphere is about 10-18).

(b) The moon's mass is 0.0123times Earth's. its radius 0.26 times Earth's, and its surface temperatures rise to 370K. Should it be able to hold on to these gases?

The maximum wavelength light that will eject electrons from metal I via the photoelectric effect is410nm. For metal2, it is280nm. What would be the potential difference if these two metals were put in contact?

Consider a room divided by imaginary lines into three equal parts. Sketch a two-axis plot of the number of ways of arranging particles versus NleftandNrightfor the caseN=1023, Note that Nmiddleis not independent, being of courseNNnghtNleftYour axes should berole="math" localid="1658331658925" NleftandNright, and the number of ways should be represented by density of shading. (A form for numbers of ways applicable to a three-sided room is given in Appendix I. but the question can be answered without it.)

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