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Chapter 7: Q1CQ (page 278)

What is a quantum number, and how does it arise?

Short Answer

Expert verified

A quantum number is a number that portrays the condition of a molecule. A bunch of quantum numbers might be expected to portray the state completely.Quantum numbers come up when we tackle the Schrodinger condition with forced limit conditions to get a genuinely satisfactory arrangement.

Step by step solution

01

Step 1:Define quantum numbers

In science and quantum physical science, quantum numbers exhibit the upsides of preserved amounts in the elements of a quantum framework. Quantum numbers are used to show the state of an atom or molecule. It gives us all the necessary information that is important to understand the nature, properties, and characteristics of the entity.

02

The rise of quantum numbers

A quantum number is a number that portrays the condition of a molecule. A bunch of quantum numbers might be expected to portray the state completely. Quantum numbers come up when we tackle the Schrodinger condition with forced limit conditions to get a genuinely satisfactory arrangement. These limit conditions led to standing waves and quantized detectable amounts (like energy) that are portrayed by quantum numbers.

The four quantum numbers are Principal quantum number, azimuthal quantum number, magnetic quantum number, and Spin quantum number. Each quantum number tells a different story about the respective atom/ molecule.The principal quantum number gives information about the shells, azimuthal quantum numbers tell us about the subshells, and magnetic and spin quantum numbers tell us about how electrons are settled in the orbits.

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Most popular questions from this chapter

Some degeneracies are easy to understand on the basis of symmetry in the physical situation. Others are surprising, or “accidental”. In the states given in Table 7.1, which degeneracies, if any, would you call accidental and why?

Classically, an orbiting charged particle radiates electromagnetic energy, and for an electron in atomic dimensions, it would lead to collapse in considerably less than the wink of an eye.

(a) By equating the centripetal and Coulomb forces, show that for a classical charge -e of mass m held in a circular orbit by its attraction to a fixed charge +e, the following relationship holds

ω=er-3/24πε0m.

(b) Electromagnetism tells us that a charge whose acceleration is a radiates power P=e2a2/6ε0c3. Show that this can also be expressed in terms of the orbit radius as P=e696π2ε03m2c3r4. Then calculate the energy lost per orbit in terms of r by multiplying the power by the period T=2π/ωand using the formula from part (a) to eliminate .

(c) In such a classical orbit, the total mechanical energy is half the potential energy, or Eorbit=-e28πε0r. Calculate the change in energy per change in r : dEorbit/dr. From this and the energy lost per obit from part (b), determine the change in per orbit and evaluate it for a typical orbit radius of 10-10m. Would the electron's radius change much in a single orbit?

(d) Argue that dividing dEorbit/dr by P and multiplying by dr gives the time required to change r by dr . Then, sum these times for all radii from rinitial to a final radius of 0. Evaluate your result for rinitial=10-10m. (One limitation of this estimate is that the electron would eventually be moving relativistically).

Question: A particle is trapped in a spherical infinite well. The potential energy is 0for r < a and infinite for r > a . Which, if any, quantization conditions would you expect it to share with hydrogen, and why?

To conserve momentum, an atom emitting a photon must recoil, meaning that not all of the energy made available in the downward jump goes to the photon. (a) Find a hydrogen atom's recoil energy when it emits a photon in a n = 2 to n = 1 transition. (Note: The calculation is easiest to carry out if it is assumed that the photon carries essentially all the transition energy, which thus determines its momentum. The result justifies the assumption.) (b) What fraction of the transition energy is the recoil energy?

Question: Consider a cubic 3D infinite well of side length of L. There are 15 identical particles of mass m in the well, but for whatever reason, no more than two particles can have the same wave function. (a) What is the lowest possible total energy? (b) In this minimum total energy state, at what point(s) would the highest energy particle most likely be found? (Knowing no more than its energy, the highest energy particle might be in any of multiple wave functions open to it and with equal probability.)
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