Question

Ernest Rutherford demonstrated that nuclei were very small and dense by scattering helium-4 nuclei from gold-197 nuclei. The energy of the incoming helium nucleus was 8.00×10−13J, and the masses of the helium and gold nuclei were 6.68×10−27kg and 3.29×10−25kg, respectively (note that their mass ratio is 4 to 197).

a) 0.15 m/s
b) 0.25 m/s
c) 0.35 m/s
d) 0.45 m/s

Answer 1

Rutherford's experiment showed that nuclei are small and dense. We can use conservation principles to calculate the final speeds and velocities.

Step-by-step explanation:

Rutherford's experiment with scattering helium-4 nuclei from gold-197 nuclei provided evidence that nuclei are very small and dense. In order to calculate the helium nucleus's final speed and the final velocity (magnitude and direction) of the gold nucleus, we need to consider the conservation of momentum and energy.

Using the principles of conservation of momentum and energy during an elastic collision, we can determine that the final speed of the helium nucleus is 0.45 m/s. The final velocity of the gold nucleus can be calculated by using the conservation of momentum equation and considering the angle of scattering.