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Animated Solution for Physics - Atoms and Nuclei: nucleus, after absorbing energy, decays into two -particles and an unknown nucleus. The unknown nucleus is

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Visualized Solution

  • \text{Initial nucleus: } ^{22}_{10}\text{Ne}
  • \text{Atomic number, } Z_i = 10
  • \text{Mass number, } A_i = 22

  • \text{Emitted: Two } \alpha\text{-particles}
  • \alpha\text{-particle} = ^{4}_{2}\text{He}
  • \text{Unknown nucleus} = ^{A}_{Z}\text{X}

  • ^{22}_{10}\text{Ne} \rightarrow 2 \, ^{4}_{2}\text{He} + ^{A}_{Z}\text{X}
  • \text{Conservation Laws:}
  • \sum Z_{\text{initial}} = \sum Z_{\text{final}}
  • \sum A_{\text{initial}} = \sum A_{\text{final}}

  • 10 = 2(2) + Z
  • 10 = 4 + Z
  • Z = 10 - 4 = 6

  • 22 = 2(4) + A
  • 22 = 8 + A
  • A = 22 - 8 = 14

  • Z = 6 \implies \text{Carbon (C)}
  • A = 14
  • \text{Unknown nucleus: } ^{14}_{6}\text{C}

  • \text{What if the decay involved } \beta\text{-particles?}
  • \text{How does energy absorption trigger this decay?}

The Sigma Insight: Radioactivity

Solution Diagram

The Mystery of the Decaying Neon

Imagine you are a nuclear detective, and you've just been handed a case. A Neon-22 nucleus has absorbed some energy and undergone a dramatic transformation. It has split apart, emitting two alpha particles and leaving behind a mysterious, unknown nucleus. Our mission? To identify this unknown remnant.
To solve this, we need to rely on the fundamental laws of nuclear physics. In any low-energy nuclear reaction, two critical quantities are always conserved: the total charge (represented by the atomic number, ) and the total number of nucleons (represented by the mass number, ).

Setting Up the Nuclear Equation

Let's start by writing down what we know. Our initial nucleus is Neon-22. If we glance at the periodic table, we find that Neon has an atomic number of 10. So, we can write it as .
Next, we look at the products of the decay. The problem tells us that two alpha particles are emitted. An alpha particle is simply a Helium nucleus, which consists of 2 protons and 2 neutrons. Therefore, its atomic number is 2 and its mass number is 4. We write this as .
Let's represent our unknown nucleus as , where is its atomic number and is its mass number. We can now construct our nuclear reaction equation:

Balancing the Equation

Now comes the detective work. We must balance the equation by applying our conservation laws. Let's start with the atomic number, . The total atomic number on the left side must equal the total atomic number on the right side.
Solving this simple algebraic equation, we get:
So, our unknown nucleus has an atomic number of 6.
Next, let's balance the mass number, . The total mass number on the left must equal the total mass number on the right.
Solving for , we find:

The Final Reveal

We have successfully calculated the properties of our unknown nucleus: it has an atomic number and a mass number .
The identity of an element is strictly determined by its atomic number. If we look at the periodic table for the element with , we find Carbon.
Therefore, the mysterious unknown nucleus is Carbon-14 (). This perfectly matches option (b). Case closed!

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