Question

Write a balanced nuclear equation for the beta decay of gold-211. Include atomic number, mass number, and symbol for each element. Explain your work?

Answer 1

The equation is `""_79^211"Au" → ""_80^211"Hg" + β`

Explanation:

Your equation is

`""_79^211"Au" → "?" + β`

It becomes easier to balance the equation if we replace the "?" with an element symbol `""_x^y"Z"`.

Then the equation becomes

`""_79^211"Au" → ""_x^y"Z"" + β`

We should also recall that a β particle is an electron. Its nuclear symbol is `""_text(-1)^0"e"`.

The equation then becomes

`""_79^211"Au" → ""_x^y"Z" + ""_text(-1)^0"e"`

The main point to remember in balancing nuclear equations is that the sums of the superscripts and the subscripts must be the same on each side of the equation.

Sum of superscripts: `211 = y + 0`, so `y =211`.

Sum of subscripts: `color(white)(ml)79 = x"-1"`, so `x = 80`.

We get

`""_79^211"Au" → ""_80^211"Z" + ""_text(-1)^0"e"`

The atomic number of the element is 80, mercury.

∴ The nuclear equation is

`""_79^211"Au" → ""_80^211"Hg" + ""_text(-1)^0"e"`

If desired, you could re-insert the β symbol and get

`""_79^211"Au" → ""_80^211"Hg" + β`

The equation is `color(blue)(""_79^211"Au" → ""_80^211"Hg" + β)`