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

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6.03 \times 1 0^{23}

5.96 \times 1 0^{23}

5.03 \times 1 0^{23}

6.203 \times 1 0^{23}

answer is B.

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Detailed Solution

The number of alpha particles that would deflect at angles less than 50 degrees are $5.96 \times 1 0^{23}$ .
Percentage of alpha particles deflected more than $50 ° = 1 %$ of alpha particles Percentage of alpha particles deflected less than $50 ° = (100 - 1$ )%
$\Rightarrow 99 %$ Number of alpha particles bombarded $= 1 mole$
$\Rightarrow 6.022 \times 1 0^{23}$
Number of alpha particles deflected less than $50 ° = \frac{99}{100} \times 6.022 \times 1 0^{23}$
$\Rightarrow 5.96 \times 1 0^{23}$ Particles