37.

(a) Since the mass of an electron is m = 9.109

× 10

−31

kg, its Compton wavelength is

λ

C

=

h

mc

=

6.626

× 10

−34

J

·s

(9.109

× 10

−31

kg)(2.998

× 10

8

m/s)

= 2.426

× 10

−12

m = 2.43 pm .

(b) Since the mass of a proton is m = 1.673

× 10

−27

kg, its Compton wavelength is

λ

C

=

6.626

× 10

−34

J

·s

(1.673

× 10

−27

kg)(2.998

× 10

8

m/s)

= 1.321

× 10

−15

m = 1.32fm .

(c) We use the formula developed in Exercise 3: E = (1240 eV

·nm)/λ, where E is the energy and λ

is the wavelength. Thus for the electron, E = (1240 eV

·nm)/(2.426 × 10

−3

nm) = 5.11

× 10

5

eV =

0.511 MeV.

(d) For the proton, E = (1240 eV

·nm)/(1.321 × 10

−6

nm) = 9.39

× 10

8

eV = 939 MeV.