Questions: Fill in the missing symbol in this nuclear chemical equation. 6^11 C rightarrow 5^11 B +

Transcript text: Fill in the missing symbol in this nuclear chemical equation. \[ { }_{6}^{11} \mathrm{C} \rightarrow{ }_{5}^{11} \mathrm{~B}+ \] $\square$

Solution

Solution Steps

Step 1: Understand the Nuclear Reaction

In a nuclear reaction, the sum of the atomic numbers (subscripts) and the sum of the mass numbers (superscripts) must be conserved. This means that the total number of protons and neutrons before the reaction must equal the total number after the reaction.

Step 2: Analyze the Given Equation

The given nuclear equation is:

\[ {}_{6}^{11} \mathrm{C} \rightarrow {}_{5}^{11} \mathrm{~B} + \square \]

The carbon nucleus ($ {}_{6}^{11} \mathrm{C} $) has 6 protons and a mass number of 11.
The boron nucleus ($ {}_{5}^{11} \mathrm{~B} $) has 5 protons and a mass number of 11.

Step 3: Determine the Missing Particle

To conserve the atomic number and mass number, we need to find a particle that, when added to boron, will result in the same atomic and mass numbers as carbon.

Atomic Number Conservation: \[ 6 = 5 + Z \] Solving for $ Z $, we find $ Z = 1 $.
Mass Number Conservation: \[ 11 = 11 + A \] Solving for $ A $, we find $ A = 0 $.

The particle with an atomic number of 1 and a mass number of 0 is a positron ($ {}_{+1}^{0} \beta $).