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Chapter 21: Problem 23

Which of the following nuclides have magic numbers of both protons and neutrons: \((\mathbf{a})\) beryllium- \(10,(\mathbf{b})\) silicon- 28 , (c) chromium-52, (d) nickel-56, (e) krypton-84?

Short Answer

Expert verified
The nuclide with magic numbers of both protons and neutrons is (d) Nickel-56 (Ni-56) with Z=28 and N=28.

Step by step solution

01

Identify Protons and Neutrons

Determine the number of protons and neutrons in each of the given nuclides. The atomic number (Z) of the element gives the number of protons, while the mass number (A) minus the atomic number gives the number of neutrons (N). a) Beryllium-10 (Be-10) Z = 4 (Atomic number of Be) A = 10 N = A - Z = 10 - 4 = 6 b) Silicon-28 (Si-28) Z = 14 (Atomic number of Si) A = 28 N = A - Z = 28 - 14 = 14 c) Chromium-52 (Cr-52) Z = 24 (Atomic number of Cr) A = 52 N = A - Z = 52 - 24 = 28 d) Nickel-56 (Ni-56) Z = 28 (Atomic number of Ni) A = 56 N = A - Z = 56 - 28 = 28 e) Krypton-84 (Kr-84) Z = 36 (Atomic number of Kr) A = 84 N = A - Z = 84 - 36 = 48
02

Check for Magic Numbers

Now, compare each of the determined values of Z and N with the magic numbers (2, 8, 20, 28, 50, 82, and 126) to see if they have magic numbers of both protons and neutrons. a) Be-10 Z = 4 (Not a magic number) N = 6 (Not a magic number) b) Si-28 Z = 14 (Not a magic number) N = 14 (Not a magic number) c) Cr-52 Z = 24 (Not a magic number) N = 28 (A magic number) d) Ni-56 Z = 28 (A magic number) N = 28 (A magic number) e) Kr-84 Z = 36 (Not a magic number) N = 48 (Not a magic number)
03

Provide the Answer

Based on the comparison above, only Nickel-56 (Ni-56) has both magic numbers of protons (Z=28) and neutrons (N=28). So, the answer is (d) Nickel-56.

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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?

Nuclear scientists have synthesized new elements and isotopes, which are not known in nature using heavy-ion bombardment techniques in high-energy particle accelerators. Complete and balance the following reactions: (a) ${ }_{6}^{12} \mathrm{C}+{ }_{6}^{12} \mathrm{C} \longrightarrow ?+{ }_{2}^{4} \mathrm{He}$ (b) \({ }_{3}^{6} \mathrm{Li}+{ }_{28}^{63} \mathrm{Ni} \longrightarrow\) ? (c) \({ }^{252} \mathrm{Cf}+{ }_{5}^{10} \mathrm{~B} \longrightarrow ?\) (d) ${ }_{92}^{238} \mathrm{U}+{ }_{6}^{12} \mathrm{C} \longrightarrow ?+4{ }_{0}^{1} \mathrm{n}$

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}$.

Which are not classified as ionizing radiation: gamma rays, beta particles, radio waves used in radio and television, and infrared radiation from sun?

What do these symbols stand for? (a) \({ }_{0}^{0} \gamma,(\mathbf{b}){ }_{2}^{4} \mathrm{He},\) (c) \({ }_{0}^{1} \mathrm{n} .\)
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