Question

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

Answer 1

Step 1: Given data

Percentage of $\mathrm{\alpha }-$particles deflected at more than ${50}^{°}=1\%$of total $\mathrm{\alpha }-$particles

Number of moles of $\mathrm{\alpha }-$particles bombarded on the gold file$=1\mathrm{mole}$

Step 2: Calculating number of $\mathrm{\alpha }-$particles deflected at less than ${50}^{°}$

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

Number of $\mathrm{\alpha }-$particles deflected at an angle greater than ${50}^{°}$$=1\%$

Number of $\mathrm{\alpha }-$particles deflected at an angle less than ${50}^{°}$$=100-1\%\Rightarrow 99\%$

$=\frac{99}{100}\times 6.022\times {10}^{22}$

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

Therefore, the number of $\mathrm{\alpha }-$particles deflected at angles less than ${50}^{°}$is $=5.96\times {10}^{23}$