Question

In Rutherford's alpha-particle scattering experiment, only a few alpha particles rebound back because:
A. The size of gold nucleus is very small as compared to the size of gold atom.
B. Alpha particle and gold nucleus have equal charge.
C. The impact parameter is minimum for a few alpha particles.
D. A few alpha particles have very high kinetic energy.
E. Only a few alpha particles undergo head-on collision with the nuclei.
Choose the correct answer from the options given below:

• A. A, B Only
• B. B, E Only
• C. C, D Only
• D. A, C, E Only

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Rutherford's scattering experiment revealed the structure of the atom. Rebounding (scattering at $180^\circ$) requires a massive repulsive force, which only happens if the alpha particle scores a direct, head-on hit with the dense, positively charged nucleus. Because the nucleus is astronomically small compared to the atom, these specific head-on paths are extremely rare.
Step 2: Key Formula or Approach:
Scattering angle $\theta$ depends on the impact parameter $b$:
$b = \frac{1}{4\pi\epsilon_0} \frac{Z e^2 \cot(\theta/2)}{K}$
For rebounding ($\theta = 180^\circ$), $\cot(90^\circ) = 0 \implies b = 0$.
Step 3: Detailed Explanation:
Let's evaluate each statement:
A. True. The nucleus is incredibly small ($\sim 10^{-15}$ m) compared to the atom ($\sim 10^{-10}$ m). Most of the atom is empty space, explaining why so few particles encounter the nucleus at all.
B. False. The alpha particle has a charge of $+2e$, whereas the gold nucleus has a charge of $+79e$. They are not equal.
C. True. The impact parameter $b$ is the perpendicular distance between the particle's initial trajectory and the parallel line running through the nucleus's center. For an alpha particle to rebound ($\theta \approx 180^\circ$), it must be aimed almost exactly at the center of the nucleus, meaning $b \approx 0$ (minimum).
D. False. A higher kinetic energy would actually make it harder to rebound completely and would allow the particle to penetrate closer to the nucleus before stopping. The number of rebounding particles is dictated by geometry (the tiny target area), not variance in particle kinetic energy (the emitted alpha particles had relatively uniform energy).
E. True. Rebounding is precisely defined as a head-on collision where the repulsive Coulomb force completely stops and reverses the particle. Because the nucleus is so small, only a few particles happen to be on a direct collision course.
Thus, statements A, C, and E are the correct physical explanations.
Step 4: Final Answer:
Options A, C, and E only are correct.