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Q11 PE

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College Physics (Urone)
Found in: Page 1149
College Physics (Urone)

College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

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Short Answer

What is the ratio of the velocity of a \({\rm{\beta }}\) particle to that of an\({\rm{\alpha }}\) particle, if they have the same nonrelativistic kinetic energy?

The ratio of the velocity of both the particles is obtained as: \(\frac{{{v_{beta}}}}{{{v_{alpha}}}} = 85.163\).

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Define Radioactivity

The spontaneous emission of radiation in the form of particles or high-energy photons as a result of a nuclear process is known as radioactivity.

Step 2: Evaluating the alpha particle 

The mass of the \({\rm{\beta }}\) particle is equal to the value of:

\({m_\beta } = 9.1 \times {10^{ - 31}}\,{\rm{kg}}\)

The mass of the \({\rm{\alpha }}\) particle is equal to:

\({m_\alpha } = 6.6 \times {10^{ - 27}}\,{\rm{kg}}\)

Solve for the \({\rm{\alpha }}\) particle:

In order to evaluate the kinetic energy, we use the relation as:

\(K.{E_\alpha } = \frac{1}{2}{m_\alpha }v_{alpha}^2\)

Step 3: Evaluating the beta particle 

Solve for the \({\rm{\beta }}\) particle:

In order to evaluate the kinetic energy, we use the relation as:

\(K.{E_\beta } = \frac{1}{2}{m_\beta }v_{beta}^2\)

As, the kinetic energy for both particles are equal, then we obtain:

\(\begin{align}K.{E_\alpha } &= K.{E_\beta }\\ &= \frac{1}{2}{m_\alpha }v_{alpha}^2\\ &= \frac{1}{2}{m_\beta }v_{beta}^2\end{align}\)

Step 3: Evaluating the ratio

Rearranging and then solving to obtain the ratio of both the particles as:

\(\begin{align}\frac{{{v_{beta}}}}{{{v_{alpha}}}} &= \sqrt {\frac{{{m_{beta}}}}{{{m_{alpha}}}}} \\ &= \sqrt {\frac{{6.6 \times {{10}^{ - 27}}\,kg}}{{9.1 \times {{10}^{ - 31}}\,kg}}} \\ &= 85.163\end{align}\)

Therefore, the ratio is: \(85.163\).

Most popular questions for Physics Textbooks

Often, when people have to work around radioactive materials spills, we see them wearing white coveralls (usually a plastic material). What types of radiation (if any) do you think these suits protect the worker from, and how?

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