Write balanced nuclear equations for the following processes: (a) radon-198 undergoes alpha emission; (b) thorium-234 undergoes beta emission; (c) copper-61 undergoes positron emission; (d) silver-106 undergoes electron capture.

In alpha emission, an alpha particle (a helium nucleus) is emitted. An alpha particle has a mass number of 4 and an atomic number of 2. We are given that the initial nucleus is Radon-198 (\(^{198}\textrm{Rn}\)), which has a mass number of 198 and an atomic number of 86. To conserve the mass number and atomic number in the equation, we subtract the values of the alpha particle from the initial nucleus: Mass number: 198 - 4 = 194 Atomic number: 86 - 2 = 84 This product nucleus has mass number 194 and atomic number 84. The element with an atomic number of 84 is Polonium (Po). Therefore, the balanced nuclear equation for this process can be written as: \[^{198}\textrm{Rn} \rightarrow ^{194}\textrm{Po} + ^4_2\textrm{He}\]

In beta emission, a beta particle (an electron) is emitted. A beta particle has a mass number of 0 and an atomic number of -1. We are given that the initial nucleus is Thorium-234 (\(^{234}\textrm{Th}\)), which has a mass number of 234 and an atomic number of 90. Mass number remains the same after the beta emission, and the atomic number increases by 1: Mass number: 234 Atomic number: 90 + 1 = 91 This product nucleus has mass number 234 and atomic number 91. The element with an atomic number of 91 is Protactinium (Pa). Therefore, the balanced nuclear equation for this process can be written as: \[^{234}\textrm{Th} \rightarrow ^{234}\textrm{Pa} + ^0_{-1}\textrm{e}\]

In positron emission, a positron (an anti-electron) is emitted. A positron has a mass number of 0 and an atomic number of +1. We are given that the initial nucleus is Copper-61 (\(^{61}\textrm{Cu}\)), which has a mass number of 61 and an atomic number of 29. Mass number remains the same after the positron emission, and the atomic number decreases by 1: Mass number: 61 Atomic number: 29 - 1 = 28 This product nucleus has mass number 61 and atomic number 28. The element with an atomic number of 28 is Nickel (Ni). Therefore, the balanced nuclear equation for this process can be written as: \[^{61}\textrm{Cu} \rightarrow ^{61}\textrm{Ni} + ^0_{+1}\textrm{e}\]

In electron capture, an electron from an atom's inner shell is captured by the nucleus. The captured electron has a mass number of 0 and an atomic number of -1. We are given that the initial nucleus is Silver-106 (\(^{106}\textrm{Ag}\)), which has a mass number of 106 and an atomic number of 47. Mass number remains the same after electron capture, and the atomic number decreases by 1: Mass number: 106 Atomic number: 47 - 1 = 46 This product nucleus has mass number 106 and atomic number 46. The element with an atomic number of 46 is Palladium (Pd). Therefore, the balanced nuclear equation for this process can be written as: \[^{106}\textrm{Ag} + ^0_{-1}\textrm{e} \rightarrow ^{106}\textrm{Pd}\]