20.

(a) Using Eq. 29-16, we obtain

v =

rqB

m

α

=

2eB

4.00 u

=

2(4.50

× 10

−2

m)(1.60

× 10

−19

C)(1.20 T)

(4.00 u)(1.66

× 10

−27

kg/u)

= 2.60

× 10

6

m/s .

(b) T = 2πr/v = 2π(4.50

× 10

−2

m)/(2.60

× 10

6

m/s) = 1.09

× 10

−7

s.

(c) The kinetic energy of the alpha particle is

K =

1

2

m

α

v

2

=

(4.00 u)(1.66

× 10

−27

kg/u)(2.60

× 10

6

m/s)

2

2(1.60

× 10

−19

J/eV)

= 1.40

× 10

5

eV .

(d) ∆V = K/q = 1.40

× 10

5

eV/2e = 7.00

× 10

4

V.