p45_039.pdf

39. (a) We substitute λ = (2898 µ m

K) /T into the result of Exercise 3 of Chapter 39: E = (1240 eV

nm) /λ .

First, we convert units: 2898 µ m

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

=(4 . 28

10 − 10 MeV / K) T.

2 . 898

10 6 nm

(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 =

10 − 10 MeV / K =

1 . 022 MeV

10 − 10 MeV / K =2 . 39

10 9 K .

4 . 28