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Chapter 21: Problem 10

Indicate the number of protons and neutrons in the following nuclei: $(\mathbf{a}){ }^{214} \mathrm{Bi},(\mathbf{b}){ }^{210} \mathrm{~Pb},(\mathbf{c})\( uranium- \)235 .$.

Short Answer

Expert verified
The number of protons and neutrons for the given nuclei are: - \(^{214}\mathrm{Bi}\): 83 protons and 131 neutrons - \(^{210}\mathrm{Pb}\): 82 protons and 128 neutrons - uranium-235: 92 protons and 143 neutrons

Step by step solution

01

Find the atomic numbers for Bi, Pb, and U.

To determine the atomic numbers for Bismuth (Bi), Lead (Pb), and Uranium (U), we can look up these elements in the periodic table. Doing so, we find the following atomic numbers: - Bismuth (Bi): Z = 83 - Lead (Pb): Z = 82 - Uranium (U): Z = 92
02

Calculate the number of protons for each nucleus.

Using the atomic numbers found in Step 1, the number of protons will be equal to the atomic number for each nucleus: - \(^{214}\mathrm{Bi}\): 83 protons - \(^{210}\mathrm{Pb}\): 82 protons - uranium-235: 92 protons
03

Calculate the number of neutrons for each nucleus.

To find the number of neutrons, subtract the atomic number (number of protons) from the mass number for each nucleus. We have the following: - \(^{214}\mathrm{Bi}\): Neutrons = A - Z = 214 - 83 = 131 neutrons - \(^{210}\mathrm{Pb}\): Neutrons = A - Z = 210 - 82 = 128 neutrons - uranium-235: Neutrons = A - Z = 235 - 92 = 143 neutrons In summary, the number of protons and neutrons for the given nuclei are: - \(^{214}\mathrm{Bi}\): 83 protons and 131 neutrons - \(^{210}\mathrm{Pb}\): 82 protons and 128 neutrons - uranium-235: 92 protons and 143 neutrons

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Most popular questions from this chapter

A \(26.00-g\) sample of water containing tritium, \({ }_{1}^{3} \mathrm{H},\) emits \(1.50 \times 10^{3}\) beta particles per second. Tritium is a weak beta emitter with a half-life of \(12.3 \mathrm{yr}\). What fraction of all the hydrogen in the water sample is tritium?

Write balanced equations for each of the following nuclear reactions: $(\mathbf{a}){ }_{92}^{238} \mathrm{U}(\mathrm{n}, \gamma){ }^{239} \mathrm{U},(\mathbf{b}){ }_{82}^{16} \mathrm{O}(\mathrm{p}, \alpha){ }^{13} \mathrm{~N},\( (c) \){ }_{8}^{18} \mathrm{O}\left(\mathrm{n}, \beta^{-}\right){ }^{19} \mathrm{~F}$.

Write balanced equations for (a) ${ }_{92}^{238} \mathrm{U}(\alpha, \mathrm{n}){ }^{241} \mathrm{Pu},$ (b) ${ }^{14} \mathrm{~N}(\alpha, \mathrm{p}){ }^{17} \mathrm{O},(\mathbf{c}){ }_{26}^{56} \mathrm{Fe}\left(\alpha, \beta^{-}\right)_{29}^{60} \mathrm{Cu} .$

A \(65-\mathrm{kg}\) person is accidentally exposed for \(240 \mathrm{~s}\) to \(\mathrm{a}\) 15-mCi source of beta radiation coming from a sample of ${ }^{90}$ Sr. (a) What is the activity of the radiation source in disintegrations per second? In becquerels? (b) Each beta particle has an energy of \(8.75 \times 10^{-14} \mathrm{~J} .\) and \(7.5 \%\) of the radiation is absorbed by the person. Assuming that the absorbed radiation is spread over the person's entire body, calculate the absorbed dose in rads and in grays. \((\mathbf{c})\) If the RBE of the beta particles is \(1.0,\) what is the effective dose in mrem and in sieverts? (d) Is the radiation dose equal to, greater than, or less than that for a typical mammogram \((3 \mathrm{mSv}) ?\)

Each statement that follows refers to a comparison between two radioisotopes, \(A\) and \(X .\) Indicate whether each of the following statements is true or false. (a) If the half-life for \(\mathrm{A}\) is shorter than the half-life for \(\mathrm{X}, \mathrm{A}\) has a larger decay rate constant. (b) If \(X\) is "not radioactive," its half-life is essentially zero. (c) If A has a half-life of 10 yr, and \(X\) has a half-life of $10,000 \mathrm{yr}$, A would be a more suitable radioisotope to measure processes occurring on the 40 -yr time scale.
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