An -particle emitted in the radioactive decay of radium has a kinetic energy of 8.0 10

An α-particle emitted in the radioactive decay of radium has a kinetic energy of 8.0 × 10⁻¹³ J.

a. i. Calculate the potential difference that an α-particle, initially at rest, would have to be accelerated through to gain this energy.

ii. Calculate the speed of the α-particle at this kinetic energy.

b. This diagram shows the path of an α-particle of this energy as it approaches a gold nucleus head-on.

i. State the speed of the α-particle at its point of closest approach to the gold nucleus.
ii. Write down the kinetic energy of the α-particle at this point.
iii. Write down the potential energy of the α-particle at this point.
c. Use your answer to part b iii to show that the α-particle will reach a distance of 4.5 × 10⁻¹⁴ m from the centre of the gold nucleus.
d. Suggest and explain what this information tells us about the gold nucleus.
(Mass of an α-particle = 6.65 × 10⁻²⁷ kg; charge on an α-particle = +2e; charge on a gold nucleus = +79e.)

Transcribed Image Text:

a-particle gold nucleus Figure 22.20