Chapter 4, Problem 66A

Interpretation Introduction

Interpretation : The percentage of the alpha particles was $5^{\circ }$ or less to be calculated.

Concept Introduction : Rutherford performed a gold foil experiment to test the atomic structure plum-pudding model.

Answer to Problem 66A

The percentage of alpha deflection was $5^{\circ }$ or less is given as $92.9\%$ .

Explanation of Solution

Given information:

The angle of deflection and number of deflections are given.

According to Rutherford’s experimental results, the majority of alpha particles either passed right through the gold foil or only minimally deflected it.

To calculate the percentage of deflections, first, calculate the total number of deflections in the gold foil experiment.

  $\begin{array}{c}\text{Total}\text{deflection}=\text{8289000+502570+120570+7800+1435+477+211+198}\\ =\text{8922261}\end{array}$

The total number of deflections is $\text{8922261}$ .

To calculate the percentage of alpha deflections, divide the number of deflections for the given angle by a total number of deflections.

The percentage of alpha deflection was $5^{\circ }$ or less is given as

  $\begin{array}{c}{5}^{\circ }=\frac{8289000}{\text{8922261}}\times 100\%\\ =0.929\times 100\%\\ =92.9\%\end{array}$

Interpretation Introduction

Interpretation : The percentage of the alpha particles was ${15}^{\circ }$ or less to be calculated.

Concept Introduction : Rutherford performed a gold foil experiment to test the atomic structure plum-pudding model.

Answer to Problem 66A

The percentage of alpha deflection was ${15}^{\circ }$ or less is given as $99.89\%$ .

Explanation of Solution

Given information:

The angle of deflection and number of deflections are given.

According to Rutherford’s experimental results, the majority of alpha particles either passed right through the gold foil or only minimally deflected it.

To calculate the percentage of deflections, first, calculate the total number of deflections in the gold foil experiment.

  $\begin{array}{c}\text{Total}\text{deflection}=\text{8289000+502570+120570+7800+1435+477+211+198}\\ =\text{8922261}\end{array}$

The total number of deflections is $\text{8922261}$ .

To calculate the percentage of alpha deflections, divide the number of deflections for the given angle by total number of deflections.

The percentage of alpha deflection was ${15}^{\circ }$ or less is given as

  $\begin{array}{c}{15}^{\circ }=\frac{\left(8289000+502570+120570\right)}{\text{8922261}}\times 100\%\\ =0.9989\times 100\%\\ =99.89\%\end{array}$

Interpretation Introduction

Interpretation : The percentage of the alpha particles was ${60}^{\circ }$ or greater to be calculated.

Concept Introduction : Rutherford performed a gold foil experiment to test the atomic structure plum-pudding model.

Answer to Problem 66A

The percentage of alpha deflection was ${60}^{\circ }$ or greater is given as $0.0099\%$ .

Explanation of Solution

Given information:

The angle of deflection and number of deflections are given.

According to Rutherford’s experimental results, the majority of alpha particles either passed right through the gold foil or only minimally deflected it.

To calculate the percentage of deflections, first, calculate the total number of deflections in the gold foil experiment.

  $\begin{array}{c}\text{Total}\text{deflection}=\text{8289000+502570+120570+7800+1435+477+211+198}\\ =\text{8922261}\end{array}$

The total number of deflections is $\text{8922261}$ .

To calculate the percentage of alpha deflections, divide the number of deflections for the given angle by total number of deflections.

The percentage of alpha deflection was ${60}^{\circ }$ or greater is given as

  $\begin{array}{c}{60}^{\circ }=\frac{\left(477+211+198\right)}{\text{8922261}}\times 100\%\\ =0.0099\%\end{array}$