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Chapter 31: Q32PE (page 1150)

Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for 尾- decay given in the equation \(_Z^A{X_N} \to _{Z - 1}^A{Y_{N + 1}} + {\beta ^ - } + {v_e}\). To do this, identify the values of each before and after the decay.

Short Answer

Expert verified

The nucleons numbers are conserved.

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

Identifying the values before and after decay

The reaction we have is:

\(_Z^A{X_N} \to _{Z - 1}^A{Y_{N + 1}} + {\beta ^ - } + {v_e}\)

The value of z is the initial charge.

The value (Z + 1} - - 1 = Z is the final charge.

As a result, charge is preserved. 2 millimeter The number of electrons in the first family is zero.

As, the value of 尾 has a final electron family number of 1 and ve has a final electron family number of - 1, the overall electron family number is zero.

As a result, the number of electron families is preserved. (2 millimeter) The initial number of nucleons is A.

The value of A + 0 + 0 = A is the number of nucleons in the final state.

As a result, the number of nucleons remains constant.

Therefore, the nucleon numbers remain conserved.

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Most popular questions from this chapter

Verify that a\(2.3 \times {10^{17}}\,{\rm{km}}\)mass of water at normal density would make a cube\(60\,{\rm{km}}\)on a side, as claimed in Example\({\rm{31}}{\rm{.1}}\). (This mass at nuclear density would make a cube\(1.0\,{\rm{m}}\)on a side.)

(a) Write the complete\({{\rm{\beta }}^{\rm{ - }}}\]decay equation for\({}^{{\rm{90}}}{\rm{Sr}}\], a major waste product of nuclear reactors. (b) Find the energy released in the decay.

When an electron and positron annihilate, both their masses are destroyed, creating two equal energy photons to preserve momentum.

(a) Confirm that the annihilation equation \({e^ + } + {e^ - } \to \gamma + \gamma \) conserves charge, electron family number, and total number of nucleons. To do this, identify the values of each before and after the annihilation.

(b) Find the energy of each纬 ray, assuming the electron and positron are initially nearly at rest.

(c) Explain why the two纬 rays travel in exactly opposite directions if the centre of mass of the electron-positron system is initially at rest.

If an electric field is substituted for the magnetic field with positive charge instead of the north pole and negative charge instead of the south pole, in which directions will the 伪, 尾, and 纬rays bend?

The ceramic glaze on a red-orange Fiesta ware plate is \({{\rm{U}}_{\rm{2}}}{{\rm{O}}_{\rm{3}}}\)and contains \({\rm{50}}{\rm{.0}}\)grams of \(^{{\rm{238}}}{\rm{U}}\), but very little \(^{{\rm{235}}}{\rm{U}}\). (a)

  1. What is the activity of the plate?
  2. Calculate the total energy that will be released by the \(^{{\rm{238}}}{\rm{U}}\)decay.
  3. If energy is worth \({\rm{12}}{\rm{.0}}\)cents per\({\rm{kW \times h}}\), what is the monetary value of the energy emitted? (These plates went out of production some 30 years ago, but are still available as collectibles.)
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