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Chapter 31: Q7 PE (page 1149)

What is the radius of an\({\rm{\alpha }}\) particle?

Short Answer

Expert verified

The radius of the \({\rm{\alpha }}\) particle is obtained as: \(1.905 \times {10^{ - 15}}\,{\rm{m}}\).

Step by step solution

01

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.

02

Evaluating the radius

The atomic mass number of the \({\rm{\alpha }}\) particle is:

\(\;A = 4\)

The radius of\({\rm{\alpha }}\)particle is:

\({R_o} = 1.2 \times {10^{ - 15}}\,{\rm{m}}\)

Using the following relation to obtain the value of radius as:

\(\begin{align}R &= \;{R_o}{A^{\frac{1}{3}}}\\ &= 1.2 \times {10^{ - 15}}\,m \times {(4)^{\frac{1}{3}}}\\ &= {\rm{ }}1.905 \times {10^{ - 15}}\,m\end{align}\)

Therefore, the radius is: \(1.905 \times {10^{ - 15}}\,{\rm{m}}\).

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Most popular questions from this chapter

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?

\({{\rm{\beta }}^{\rm{ + }}}\)decay of \(^{{\rm{52}}}{\rm{Fe}}\)

(a) Calculate the radius of\(^{{\rm{58}}}{\rm{Ni}}\), one of the most tightly bound stable nuclei. (b) What is the ratio of the radius of\(^{{\rm{58}}}{\rm{Ni}}\)to that of\(^{{\rm{258}}}{\rm{Ha}}\), one of the largest nuclei ever made? Note that the radius of the largest nucleus is still much smaller than the size of an atom.

a) Write the complete \({{\rm{\beta }}^{\rm{ + }}}\) decay equation for \({}^{{\rm{11}}}{\rm{C}}\).(b) Calculate the energy released in the decay. The masses of \({}^{{\rm{11}}}{\rm{C}}\) and\({}^{{\rm{11}}}{\rm{B}}\) are \(11.011433\) and\(11.009305\,{\rm{u}}\) , respectively.

Construct Your Own Problem

Consider the decay of radioactive substances in the Earth's interior. The energy emitted is converted to thermal energy that reaches the earth's surface and is radiated away into cold dark space. Construct a problem in which you estimate the activity in a cubic meter of earth rock? And then calculate the power generated. Calculate how much power must cross each square meter of the Earth's surface if the power is dissipated at the same rate as it is generated. Among the things to consider are the activity per cubic meter, the energy per decay, and the size of the Earth.

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