In the gold foil experiment of Geiger and Marsden, that paved the way for Rutherford’s model of an atom, $\sim$1.00% of the $\alpha$-particles were found to deflect at angles > 50°. If one mole of a-particles were bombarded on the gold foil, compute the number of $\alpha$-particles that would deflect at angles less than 50°.

Percentage of $\alpha -$ particles deflected by more than $50^{o}=1\; ^{o}/_{o}$ of total $\alpha -$ particles.

Percentage of $\alpha -$ particles deflected by less than $50^{o}=100\; ^{o}/_{o}-1\; ^{o}/_{o}=99\; ^{o}/_{o}$ of total $\alpha -$ particles.

Number of $\alpha -$ particles bombarded on the gold foil = 1 mole $=6.022\times 10^{23}$

Number of particles that deflected by an angle less than 50°

$=\frac{99}{100}\times6.022 \times10^{23}$

$=\frac{596.178}{100}\times 10^{23}$

$=5.96 \times 10^{23}$

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