gold can undergo transmutation. which equation could correctly describe this radioactive decay?\n$_{79}^{185}…

gold can undergo transmutation. which equation could correctly describe this radioactive decay?\n$_{79}^{185}au\\rightarrow_{77}^{181}re + _{2}^{4}he$\n$_{79}^{185}au\\rightarrow_{77}^{181}ir + _{2}^{4}he$\n$_{79}^{185}au\\rightarrow_{77}^{181}ir + _{-1}^{0}e$\n$_{79}^{185}au\\rightarrow_{77}^{181}ir + _{+1}^{0}e$\ndone

gold can undergo transmutation. which equation could correctly describe this radioactive decay?\n$_{79}^{185}au\\rightarrow_{77}^{181}re + _{2}^{4}he$\n$_{79}^{185}au\\rightarrow_{77}^{181}ir + _{2}^{4}he$\n$_{79}^{185}au\\rightarrow_{77}^{181}ir + _{-1}^{0}e$\n$_{79}^{185}au\\rightarrow_{77}^{181}ir + _{+1}^{0}e$\ndone

Answer

Explanation:

Step1: Check mass - number conservation

In radioactive decay, the sum of mass - numbers on the left - hand side of the equation should equal the sum of mass - numbers on the right - hand side. For the gold transmutation reactions, the mass number of $^{185}{79}\text{Au}$ is 185. In the first option, $185 = 181+4$. In the second option, $185 = 181 + 4$. In the third and fourth options, $185=181 + 0$ (since the mass number of an electron ${- 1}^0e$ or a positron $_{+1}^0e$ is 0).

Step2: Check atomic - number conservation

The atomic number of $^{185}{79}\text{Au}$ is 79. In the first option, $79\neq77 + 2$. In the second option, $79\neq77+2$. In the third option, $79=77+( - 1)$ which is incorrect as it implies a decrease in atomic number by 2 in an incorrect way. In the fourth option, $79 = 77+2$ (since a positron ${+1}^0e$ emission increases the atomic number by 1 and the correct decay of gold can involve positron emission to change its atomic number and mass number in a consistent way).

Answer:

$^{185}{79}\text{Au}\rightarrow^{181}{77}\text{Ir}+^{0}_{+ 1}\text{e}$