Question
Explain Rutherford's argument for scattered $\alpha$-particles.

Answer

In $\alpha$-particle scattering experiment most $\alpha$-particles pass through without being detected.
Only about $0.14 \% \alpha$-particles scatter by more than $1^{\circ}$ and about 1 in 8000 deflect by more than $90^{\circ}$.
For this Rutherford argued that for the $\alpha$-particle to be deflected backwards it must experience a large repulsive force.
This is possible only when almost entire mass of the atom is concentrated in its center and this center is positively charged.
Then incoming $\alpha$-particle could get very close to the positive charge without penetrating it and such a close encounter would result in a large deflection.
This agreement supported the hypothesis of the nuclear atom. This is why Rutherford is credited with the discovery of the nucleus.

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