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 .