Question :

Draw a plot of α-particle scattering by a thin foil of gold to show the variation of the number of the scattered particles with scattering angle. Describe briefly how the large angle scattering explains the existence of the nucleus inside the atom, Explain with the help of impact parameter picture, how Rutherford scattering serves a powerful way to determine an upper limit on the size of the nucleus.




Class 12



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Answer / Solution

From the plot it is clear that most of the α-particles passed through the foil. Only 0.14% of the incident α particles scatter by more than 1% and about 1 in 8000 deflect by more than 90° α-particles deflected backward due to strong repulsive force. This force will come from positive charge concentrated at the centre as most of the particles get deflected by small angles.

The α-particles trajectory depends on collision's impact parameter (b) for a given beam of α-particles, distribution of impact parameters as beam gets scattered in different directions with different probabilities.

The figure above shows α-particle close to the nucleus suffers large scattering. Impact parameter is minimum for head-on collision α-particles rebound by 180°.

The impact parameter is high, for undeviated α-particles. With deflection angle ≈ 0°.

As these of nucleus was 10–14 m to 10–15 m w.r.t. 10–10 m in size of an atom which is 10,000 to 100,000 times larger. Hence most of the space is empty, only a small percentage of the incident particles rebound back indicates that the number of α-particle goes head-on collision. Hence most of the mass of the atom is concentrated in a small volume.

Thus, Rutherford scattering is a strong tool to determine the upper limit to the size of the nucleus.

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