Questions: Write the identity of the missing nucleus for the following nuclear decay reaction: ? -> Be (8 protons, 4 neutrons) + e (1 proton, 0 neutrons) Express your answer as an isotope.

Write the identity of the missing nucleus for the following nuclear decay reaction:
? -> Be (8 protons, 4 neutrons) + e (1 proton, 0 neutrons)

Express your answer as an isotope.

Transcript text: Write the identity of the missing nucleus for the following nuclear decay reaction: \[ ? \rightarrow{ }_{4}^{8} \mathrm{Be}+{ }_{1}^{0} \mathrm{e} \] Express your answer as an isotope.

Solution

Solution Steps

Step 1: Understand the Nuclear Decay Reaction

The given nuclear decay reaction is: \[ ? \rightarrow{ }_{4}^{8} \mathrm{Be}+{ }_{1}^{0} \mathrm{e} \]

This indicates that an unknown nucleus decays into beryllium-8 (\( _{4}^{8} \mathrm{Be} \)) and a positron (\( _{1}^{0} \mathrm{e} \)).

Step 2: Apply Conservation Laws

In nuclear reactions, both the atomic number (subscript) and the mass number (superscript) must be conserved.

Mass Number Conservation: The mass number on the left must equal the sum of the mass numbers on the right. \[ A = 8 + 0 = 8 \]
Atomic Number Conservation: The atomic number on the left must equal the sum of the atomic numbers on the right. \[ Z = 4 + 1 = 5 \]

Step 3: Identify the Missing Nucleus

The missing nucleus must have a mass number \( A = 8 \) and an atomic number \( Z = 5 \). The element with atomic number 5 is boron (B).

Thus, the missing nucleus is boron-8 (\( _{5}^{8} \mathrm{B} \)).