Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2021 / Paper 2A / Section A / 16 / b

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- Solution b

Solution

For

B ≫ Δ_{o}

, the corresponding asymptotic expansion is

225 B^{2} + 18 B Δ_{o} + Δ_{o}^{2} = 15 B + \frac{3}{5} Δ_{o} + \frac{8 Δ _{o}^{2}}{375 B} + \dots .

Hence

E_{0} E_{1} E_{2} E_{3} = - \frac{3}{5} Δ_{o} - \frac{4 Δ _{o}^{2}}{375 B} + \dots, = \frac{1}{5} Δ_{o}, = 15 B + \frac{4 Δ _{o}^{2}}{375 B} + \dots, = \frac{6}{5} Δ_{o} .

At zero field,

E_{0}, E_{1}, E_{3}

converge to the

^{3} F

atomic term and

E_{2}

to

^{3} P

at

15 B

. The

^{3} T_{1 g} (P)

branch therefore has zero initial slope; its high-field slope is not zero.

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