Question

Question #24457

Answer 1

This is how I see it.

Explanation:

Once the `"Be"` nucleus has absorbed the α particle, the new nucleus can

• do nothing
• emit a neutron
• emit an electron
• emit a proton

Let's examine each of these possibilities.

(a) Do nothing

The reaction would be

`color(white)(mmmmmm)""_4^9"Be"color(white)(l) +color(white)(ll) _2^4"He" → color(white)(ll)_6^13"C"`
`"Mass/u":color(white)(m)underbrace(9.0122color(white)(m)4.0035)_color(red)(13.0157)color(white)(m)13.0034`

We see that mass of `("Be-9 + He-4")` is 0.0103 u greater than the mass of `"C-13"`.

This small mass difference corresponds to about `10^12 color(white)(l)"J/mol"`.

Thus, each carbon-12 atom must get rid of an enormous amount of energy to become stable.

(b) Eject a neutron

This is what the nucleus does.

`""_4^9"Be" +"" _2^4"He" → ""_6^12"C" + ""_0^1"n"`

By emitting an energetic neutron, the nucleus sheds most of that energy.

(c) Eject an electron

The reaction would be

`""_4^9"Be" +"" _2^4"He" → ""_7^13"N" + ""_text(-1)^0"e"`

The nitrogen-13 is an unstable nucleus. Its radioactive half-life is about 10 ms.

(d) Eject a proton

The reaction would be

`""_4^9"Be" +"" _2^4"He" → ""_5^12"B" + ""_1^1"H"`

The boron-12 nucleus also unstable, with a half-life of about 20 ms.

Thus, ejection of a neutron is the most favourable option.