Question

In the Gold foil experiment of Geiger and Marsden, that paved the way for Rutherford's model of an atom, ~ 1.00% of the $\alpha$-particles were found to deflect at angles > ${50}^0$. 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 ${50}^0$.

• A. $7.96\times {10}^{23}$
• B. $6.96\times {10}^{23}$
• C. $5.96\times {10}^{23}$
• D. $4.96\times {10}^{23}$

Answer 1

Answer: (C)

$5.96\times {10}^{23}$

% of $\alpha$ -particles deflected more than ${50}^o$ $=$ $1$% of $\alpha$ -particles.

% of $\alpha$ -particles deflected less than ${50}^o$ $=100-1=99$%

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

Number of particles that deflected at an angle less than ${50}^o$
$=\frac{99}{100}\times 6.022\times {10}^{23}$

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

$=5.96\times {10}^{23}$

Option C is correct.