Worksheet: Rutherford Scattering

In this worksheet, we will practice calculating the distance of closest approach between two charged objects by considering energy conservation.

Q1:

A proton is fired with an initial speed of 150 m/s directly toward a fully ionized lithium nucleus that is stationary and cannot move. What is the distance of closest approach of the proton to the lithium nucleus? Use a value of 1 . 6 7 × 1 0 kg for the mass of the proton. Give your answer to 3 significant figures.

  • A 6 . 1 4 × 1 0 m
  • B 1 . 8 4 × 1 0 m
  • C 4 . 2 5 × 1 0 m
  • D 3 . 6 8 × 1 0 m
  • E 1 . 2 3 × 1 0 m

Q2:

An alpha particle is fired with an initial speed of 300 m/s directly toward a fully ionized gold nucleus that is stationary and cannot move. What is the distance of closest approach of the alpha particle to the gold nucleus? The initial potential energy of the alpha particle is negligible. Use a value of 6 . 6 4 × 1 0 kg for the mass of the alpha particle. Give your answer to 3 significant figures.

  • A 1 . 2 2 × 1 0 m
  • B 1 . 5 4 × 1 0 m
  • C 0 . 3 0 5 × 1 0 m
  • D 0 . 6 1 0 × 1 0 m
  • E 0 . 7 7 2 × 1 0 m

Q3:

A proton is fired with an initial speed of 100 m/s directly toward another proton that is stationary and cannot move.

What is the initial kinetic energy of the first proton? Use a value of 1 . 6 7 × 1 0 kg for the mass of a proton. Give your answer to 3 significant figures.

  • A 8 . 3 5 × 1 0 J
  • B 8 . 3 5 × 1 0 J
  • C 1 . 6 7 × 1 0 J
  • D 1 . 6 7 × 1 0 J
  • E 8 . 3 5 × 1 0 J

What is the distance of the closest approach of the first proton to the second? Give your answer to 3 significant figures.

  • A 1 . 3 8 × 1 0 m
  • B 1 . 3 8 × 1 0 m
  • C 2 . 7 6 × 1 0 m
  • D 2 . 7 6 × 1 0 m
  • E 2 . 7 6 × 1 0 m

Q4:

An alpha particle is fired with an initial speed of 800 m/s directly toward a fully ionized carbon nucleus that is stationary and cannot move.

What is the initial kinetic energy of the alpha particle? Use a value of 6 . 6 4 × 1 0 kg for the mass of an alpha particle. Give your answer to 3 significant figures.

  • A 2 . 1 2 × 1 0 J
  • B 4 . 2 5 × 1 0 J
  • C 2 . 6 6 × 1 0 J
  • D 5 . 3 1 × 1 0 J
  • E 3 . 5 9 × 1 0 J

What is the distance of closest approach of the alpha particle to the carbon nucleus? Give your answer to 3 significant figures.

  • A 1.30 μm
  • B 326 nm
  • C 0.651 μm
  • D 653 nm
  • E 218 nm

Q5:

An alpha particle is fired toward a fully ionized gold nucleus. The figure shows five possible paths along which the alpha particle could initially move. For which path would the alpha particle undergo the greatest deflection due to the gold nucleus?

  • A 𝐶
  • B 𝐸
  • C 𝐵
  • D 𝐷
  • E 𝐴

Q6:

An alpha particle is fired directly toward a fully ionized gold nucleus that is stationary and cannot move. At what speed must the alpha particle be fired in order for its distance of closest approach to be 20 nm? The initial potential energy of the alpha particle is negligible. Use a value of 6 . 6 4 × 1 0 kg for the mass of an alpha particle. Give your answer to 3 significant figures.

Q7:

A proton is fired directly toward another proton that is stationary and cannot move. At what speed must the first proton be fired in order for its distance of closest approach to be 10 nm? The initial potential energy between the two protons is negligible. Use a value of 1 . 6 7 × 1 0 kg for the mass of a proton and a value of 1 . 6 0 × 1 0 C for the charge of a proton. Give your answer to 3 significant figures.

  • A 5,250 m/s
  • B 6,520 m/s
  • C 7,430 m/s
  • D 3,720 m/s
  • E 4,890 m/s

Q8:

An alpha particle is fired toward a fully ionized gold nucleus. The figure shows five possible paths along which the alpha particle could initially move. For which path would the alpha particle undergo the least deflection due to the gold nucleus?

  • APath D
  • BPath E
  • CPath B
  • DPath C
  • EPath A

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