In the form of radioactive decay known as alpha decay, an unstable nucleus emits

Question

In the form of radioactive decay known as alpha decay,an unstable nucleus emits a helium-atom nucleus, which is called an alpha particle. An alpha particle contains two protons and two neutrons, thus having mass m=4uand charge q=2e. Suppose a uranium nucleus with 92 protons decays into thorium, with 90 protons, and an alpha particle. The alpha particle is initially at rest at the surface of the thorium nucleus, which is 15 fm in diameter.

What is the speed of the alpha particle when it is detected in the laboratory? Assume the thorium nucleus remains at rest.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Q = charge on thorium nucleus = 90 x 1.6 x 10-19 C

q = charge on alpha particle = 2 x 1.6 x 10-19 C

r = radius = diameter/2 = 15 fm/2 = 7.5 fm = 7.5 x 10-15 m

m = mass of alpha partilce = 4 x 1.67 x 10-27 kg

V = speed of alpha particle

total distance initially between nucleus and alpha particle = r = 7.5 x 10-15 m

using conservation of energy

Kinetic energy of proton = Electric potential energy of system at closest approach

(0.5) m v2 = k Qq/r

(0.5) (4 x 1.67 x 10-27 ) v2 = (9 x 109) (90 x 1.6 x 10-19 ) (2 x 1.6 x 10-19 ) / 7.5 x 10-15

v = 4.1 x 107 m/s

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.