39.
(a) We substitute λ = (2898 µm
·K)/T into the result of Exercise 3 of Chapter 39: E = (1240 eV·nm)/λ.
First, we convert units: 2898 µm
·K = 2.898 × 10
6
nm
·K and 1240 eV·nm = 1.240 × 10
−3
MeV
·nm.
Hence,
E =
(1.240
× 10
−3
MeV
·nm)T
2.898
× 10
6
nm
·K
= (4.28
× 10
−10
MeV/K)T .
(b) The minimum energy required to create an electron-positron pair is twice the rest energy of an
electron, or 2(0.511 MeV) = 1.022 MeV. Hence,
T =
E
4.28
× 10
−10
MeV/K
=
1.022 MeV
4.28
× 10
−10
MeV/K
= 2.39
× 10
9
K .