d) All anions are larger than their parent atoms and all cations are smaller, compare Be2+(27 pm) and Be (112pm), I-(206pm) and I(133) – please note that ionic radius depends on coordination number of ion
e) Ionic radii generally decrease with increasing positive charge on the same ion (Tl+, 164pm > Tl3+, 88pm)
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5) Electronegativity
The electronegativity of an atom is a measure of its power when in chemical combination to attract electrons to itself
With few exceptions, electronegativity increases across the periodic table and decreases down a group,
F is far more electronegative than I
F is far more electronegative than Li
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1) Revisit: The Born Interpretation
The wave function is normalised so that:
where the integration is over all space accessible to the electron. This expression simply shows that the probability of finding the electron somewhere must be 1 (100%).
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2) Radial Wavefunctions
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r
z
y
x
dr
rdq
rsinqdf
df
f
q
q
r
rsinq
The radius of the latitude is
Remember that the arc length, s, is given by s = r a (with a in radians)
The Volume Element follows hence as dV = rsinqdfrdqdr = r2sinqdfdqdr
3) Volume Element in spherical coordinates
The Surface Element follows hence as dA = rsinqdfrdq = r2sinqdfdq
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4) Pauli Principle
Yfermion (2,1) = - Yfermion (1,2)
Yboson (2,1) = Yboson (1,2)
When the labels of any two identical fermions are exchanged, the total wavefunction changes sign.
When the labels of any two identical bosons are exchanged the total wavefunction retains the same sign.
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Two particles (fermions)
Y(1,2) =y(1)y(2) s(1,2)
Total wave function of particles 1 and 2
Space wave functions of particles 1 and 2 residing in the same orbital (characterized by the same n, l, ml)
Total Spin wave function of particles 1 and 2
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Now exchanging labels
As it is just a product and a x b = b x a!
Y(1,2) =y(1)y(2) s(1,2)
And in y that is easy:
y(1)y(2) = y(2)y(1)