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Chapter 31: Q24PE (page 1149)

伪 decay of226Ra ,another isotope in the decay series of238U , first recognized as a new element by the Curies. Poses special problems because its daughter is a radioactive noble gas. In the following four problems, identify the parent nuclide and write the complete decay equation in the \(_{\rm{Z}}^{\rm{A}}{{\rm{X}}_{\rm{N}}}\) notation. Refer to the periodic table for values of Z .

Short Answer

Expert verified

The alpha Decay equation of 226Ra is \(_{88}^{226}R{a_{138}} \to _{86}^{222}R{n_{136}} + _2^4H{e_2}\).

Step by step solution

01

What is atomic mass number?

The amount of matter contained in an atom of an element is called its atomic mass.

02

Formula to be used

A = N + Z

Where A is atomic mass number

Z is the number of protons in a nucleus

X is the symbol for the element

In the expression below:

\(_Z^A{X_N}\)

Z is the number of protons in a nucleus

X is the symbol for the element

03

To determine the alpha decay equation of

226Ra

We know that

A = N + Z

Where A is atomic mass number

The atomic mass of \(_{88}^{226}R{a_{138}}\) is 226 and

A = 226 Z = 88 N = 138

Thus,

A = 222 N = 138 - 2 = 136 Z = 88 - 2 = 86

Therefore, alpha Decay equation of 226Ra is \(_{88}^{226}R{a_{138}} \to _{86}^{222}R{n_{136}} + _2^4H{e_2}\).

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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?

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.

Unreasonable Results

The manufacturer of a smoke alarm decides that the smallest current of \({\rm{\alpha }}\) radiation he can detect is \(1.00\,\mu A\).

  1. Find the activity in curies of an \({\rm{\alpha }}\) emitter that produces a \(1.00\,\mu A\)current of \({\rm{\alpha }}\) particles.
  2. What is unreasonable about this result?
  3. What assumption is responsible?

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.)

A 5000-Ci \({}^{60}Co\) source used for cancer therapy is considered too weak to be useful when its activity falls to 3500 Ci. How long after its manufacture does this happen?
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