Question

You’re designing a bubble chamber with a 1.10 Tmagnetic field. How large should it be to observe the complete circular path of the following types of particles, each having 1.9 keV kinetic energy?

Part A

Electrons.

Part B

Protons.

Part C

Alpha particles.

Answer 1

A)

B = magnetic field = 1.10 T

m = mass of electron = 9.1 x 10^-31 kg

KE = 1.9 keV = 1.9 x 1.6 x 10^-19 x 10³ = 3.04 x 10^-16 J

KE is given as :

(0.5) m v² = 3.04 x 10^-16

(0.5) (9.1 x 10^-31)v² = 3.04 x 10^-16

V = 2.585 x 10⁷ m/s

the radius of the circle is given as

r = mv/qB

r = (9.1 x 10^-31) (2.585 x 10⁷) / (1.6 x 10^-19 x 1.10 )

r = 1.34 x 10^-4 m

B)

m = mass of protons = 1.67 x 10^-27 kg

KE = 1.9 keV = 1.9 x 1.6 x 10^-19 x 10³ = 3.04 x 10^-16 J

KE is given as :

(0.5) m v² = 3.04 x 10^-16

(0.5) (1.67 x 10^-27)v² = 3.04 x 10^-16

V = 6.034 x 10⁵ m/s

the radius of the circle is given as

r = mv/qB

r = (1.67 x 10^-27) (6.034 x 10⁵ ) / (1.6 x 10^-19 x 1.10 )

r = 0.00573 m

C)

m = mass of alpha particle = 6.64 x 10^-27 kg

KE = 1.9 keV = 1.9 x 1.6 x 10^-19 x 10³ = 3.04 x 10^-16 J

KE is given as :

(0.5) m v² = 3.04 x 10^-16

(0.5) (6.64 x 10^-27)v² = 3.04 x 10^-16

V = 3.026 x 10⁵ m/s

the radius of the circle is given as

r = mv/qB

r = (6.64 x 10^-27) (3.026 x 10⁵) / (3.2 x 10^-19 x 1.10 )

r = 0.00571 m