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Chapter 21: Problem 12

Write balanced nuclear equations for the following transformations: (a) gold-191 undergoes electron capture; (b) gold-201 decays to a mercury isotope; (c) gold198 undergoes beta decay; (d) gold-188 decays by positron emission.

Short Answer

Expert verified
(a) \(Au-191 + e^- \rightarrow Ir-191 + \nu_e\) (b) \(Au-201 \rightarrow Hg-201 + e^- + \bar{\nu}_e\) (c) \(Au-198 \rightarrow Hg-198 + e^- + \bar{\nu}_e\) (d) \(Au-188 \rightarrow Ir-188 + e^+ + \nu_e \)

Step by step solution

01

(a) Gold-191 Electron Capture

In electron capture, a proton in the nucleus captures an electron from an inner atomic shell. The proton is then converted into a neutron, while a neutrino is emitted. The atomic number decreases by one, while the mass number remains unchanged. For gold-191 (Au-191) undergoing electron capture, the balanced nuclear equation is: \(Au-191 + e^- \rightarrow Ir-191 + \nu_e\)
02

(b) Gold-201 Decay to a Mercury Isotope

For gold-201 (Au-201) decaying to a mercury isotope (Hg), we must consider the most common decay mode for this isotope, which is beta-minus decay. In beta-minus decay, a neutron in the nucleus is converted into a proton, and an electron (beta particle) and an electron antineutrino are emitted. The atomic number increases by one, while the mass number remains unchanged. The balanced nuclear equation for gold-201 decaying to mercury is: \(Au-201 \rightarrow Hg-201 + e^- + \bar{\nu}_e\)
03

(c) Gold-198 Beta Decay

In beta-minus decay, a neutron in the nucleus is converted into a proton, and an electron (beta particle) and an electron antineutrino are emitted. The atomic number increases by one, while the mass number remains unchanged. For gold-198 (Au-198) undergoing beta decay, the balanced nuclear equation is: \(Au-198 \rightarrow Hg-198 + e^- + \bar{\nu}_e\)
04

(d) Gold-188 Positron Emission

In positron emission, a proton in the nucleus is converted into a neutron, and a positron and a neutrino are emitted. The atomic number decreases by one, while the mass number remains unchanged. For gold-188 (Au-188) undergoing positron emission, the balanced nuclear equation is: \(Au-188 \rightarrow Ir-188 + e^+ + \nu_e \)

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