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(a) Table 22.1 highlights important concepts associated with an electron. Associate each concept with a behavior of an electron.
(b) Derive the equation for the De Broglie wavelength.
S7P2A21 (Identity - Physical Property)
Pj Problem of Interest is of type identity (physical property). Identity of electron behaviors
(a)i Niels Bohr is credited with the postulation of energy levels in an atom. The Bohr Model of the atom assumes that electrons move in orbits around the nucleus of the atom and that each orbit has an energy associated with it. Modern quantum mechanics no longer accept this view of the motion of electrons in orbits around the nucleus. However, it retains the concept of
(ii) Louis De Broglie is credited with the discovery of the De Broglie wavelength of the electron. It established the wave behavior of the electron.
(iii) Werner Heisenberg is credited with the discovery of the Heisenberg Uncertainty Principle. The electron moves in a manner that makes it impossible to accurately know simultaneously, its momentum and position. However, the probability of its being in a given position can be calculated.
(iv) Wolfgang Pauli is credited with the discovery of the Pauli Exclusion Principle. An electron prefers to live with no more than one other electron in an orbital (their residence). The electrons must not be exactly the same. In technical terms, an orbital can hold a maximum of two electrons and they must have opposite spins.
(v) Hund is credited with the discovery of Hund's Rule. An electron prefers an empty orbital that has not been occupied by an electron like itself so it will reside in an empty orbital before pairing up with another electron with the same spin in another orbital. In technical terms, for degenerate orbitals (subshells), the lowest energy is attained when the number of electrons with the same spin is maximized
(b) De Broglie used three equations to derive the De Broglie wavelength:
E = mc2 ---------(1) Einstein' energy equation
ν = c/λ ------(2) equation for the frequency of light
E = νh ----------(3) Planck's energy equation of a photon
E is Energy; m is mass; where ν is frequency of light, c is velocity of light; λ is wavelength of light, and h is Planck's constant.
From equation (2) λ = c/ν ---------(4)
Substituting the expression for ν in (3), in (4) we have:
λ = ch/E -----------(5)
Substituting the expression for E in (1), in (5) we have:
&lamda; = ch/mc2 = h/mc ----------(6)
De Broglie replaced velocity of light c, with velocity of the electron, v
So, the De Broglie wavelength = λ = h/mv
where m is the mass of the electron, λ the wavelength of the electron and v the velocity of the electron.
The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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