b) Show that the pressure of degenerate electrons is given by 8π 3h³ me where you may use the following expression P P = and up is the velocity corresponding to momentum p. PF - or 4 p¹ (1+p²/m² c²) ∞ 1/3/[ n(p)pv, dp, -dp,
b) Show that the pressure of degenerate electrons is given by 8π 3h³ me where you may use the following expression P P = and up is the velocity corresponding to momentum p. PF - or 4 p¹ (1+p²/m² c²) ∞ 1/3/[ n(p)pv, dp, -dp,
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Transcribed Image Text:b) Show that the pressure of degenerate electrons is given by
PF
8T
p¹
dp,
3h³²m² So ² (1 + P² /m²c²") "
me
where you may use the following expression
P
=
P
and Up is the velocity corresponding to momentum p.
1
== f**n (p)pvp.dp,
=
3
Transcribed Image Text:Question 2
This question concerns electron degeneracy pressure inside white dwarfs.
a) With reference to the Fermi momentum, pF, explain what is meant by a completely degenerate electron gas. Show that the
number density of electrons in such a gas is
ne (p)dp=
Show that the total electron number density is given by
For full marks, explain all steps in your derivation.
ne
=
=
8πр²
dp
h.³
8π
3h3 pp.
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