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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

Exercise 81 obtained formulas for hydrogen like atoms in which the nucleus is not assumed infinite, as in the chapter, but is of massm1, whilem2is the mass of the orbiting negative charge. In positronium, an electron orbits a single positive charge, as in hydrogen, but one whose mass is the same as that of the electron -- a positron. Obtain numerical values of the ground state energy and “Bohr radius” of positronium.

An electron is trapped in a quantum dot, in which it is continued to a very small region in all three dimensions, If the lowest energy transition is to produce a photon of 450nm wavelength, what should be the width of the well (assumed cubic)?

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.)

Exercise 80 discusses the idea of reduced mass. When two objects move under the influence of their mutual force alone, we can treat the relative motion as a one particle system of mass μ=m1v2/(m1+m2). Among other things, this allows us to account for the fact that the nucleus in a hydrogen like atom isn’t perfectly stationary, but in fact also orbits the centre of mass. Suppose that due to Coulomb attraction, an object of mass m2and charge -eorbits an object of mass m1 and charge +Ze . By appropriate substitution into formulas given in the chapter, show that (a) the allowed energies are Z2μmE1n2, where is the hydrogen ground state, and (b) the “Bohr Radius” for this system is mzμa0 ,where a0is the hydrogen Bohr radius.

Using the functions given in Table 7.4, verify that for the more circular electron orbit in hydrogen (i.e.,l=n-1), the radial probability is of the form

P(r)∝r2ne-2r/nao

Show that the most probable radius is given by

rmostprobable=n2ao

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