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Atomic Structure and Periodic Trends
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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

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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Atomic Structure and Periodic Trends

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Appendices

Appendices

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1) Revisit: The Born Interpretation

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

2) Radial Wavefunctions

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r

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

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)

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

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)

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