Sodium vapour introduced into a flame (the classic yellow flame test) has an atom…

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · The plasma state and single-particle motion · The plasma state and single-particle motion

Plasma Physics, Ch What makes an ionised gas a plasma: shielding, the plasma parameter and the natural frequencies

Problem

Sodium vapour introduced into a flame (the classic yellow flame test) has an atom density (neutrals plus ions) of

n = 1.0\times10^{20}\,\mathrm{m^{-3}}

at a flame temperature of

T = 2000\,\mathrm{K}

. The first ionisation energy of sodium is

U = 5.14\,\mathrm{eV}

, and its ground-state degeneracies are

g_n = 2

(neutral) and

g_i = 1

(ion), the same ratio as for hydrogen, so the Saha equation may again be evaluated with

2.41\times10^{21}\,T[\mathrm{K}]^{3/2}\,\mathrm{m^{-3}}

in place of

2g_i/g_n(2\pi m_ek_BT/h^2)^{3/2}

. Assume the sodium is the only appreciable source of free electrons, so that

n_e = n_i

. ((a)) Assuming Saha equilibrium, find the fractional ionisation

x = n_i/n

of the sodium vapour. ((b)) Someone claims the yellow line seen in the flame proves that a substantial fraction of the sodium is ionised. Use the result of part (a) to say whether this is right.

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