Potassium vapour in a discharge lamp has a total atom density (neutrals plus ions) of…

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

Potassium vapour in a discharge lamp has a total atom density (neutrals plus ions) of

n = 1.0\times10^{22}\,\mathrm{m^{-3}}

and a temperature of

T = 2500\,\mathrm{K}

. The first ionisation energy of potassium is

U = 4.34\,\mathrm{eV}

. The neutral atom's ground state has degeneracy

g_n = 2

and the ion's ground state has degeneracy

g_i = 1

, the same ratio as for hydrogen, so the Saha equation may be evaluated with the same constant,

2g_i/g_n \times (2\pi m_ek_BT/h^2)^{3/2} = 2.41\times10^{21}\,T[\mathrm{K}]^{3/2}\,\mathrm{m^{-3}}

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

n_e = n_i

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

x = n_i/n

. ((b)) State, in one sentence, why this fraction is not negligible even though

k_BT

is only about one twentieth of

U

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