Balanced Nuclear Equation For Beta Minus Decay Of Co-60

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Understanding Beta Minus Decay and Nuclear Equations

In the realm of nuclear chemistry, understanding the different types of radioactive decay is crucial. Beta minus decay, also known as Ξ²- decay, is a type of radioactive decay where a neutron in the nucleus is transformed into a proton, and an electron (beta particle) and an antineutrino are emitted. This process results in an increase in the atomic number of the nucleus by one, while the mass number remains unchanged. Comprehending the fundamental principles of beta minus decay is essential for correctly interpreting and balancing nuclear equations. These equations provide a symbolic representation of nuclear reactions, illustrating the transformations that occur at the atomic level. A balanced nuclear equation must adhere to the laws of conservation, ensuring that both the mass number (the sum of protons and neutrons) and the atomic number (the number of protons) are conserved on both sides of the equation. This means that the total number of nucleons (protons and neutrons) and the total charge must be the same before and after the decay. In the context of beta minus decay, this conservation principle dictates how the parent nucleus transforms into the daughter nucleus, along with the emission of a beta particle and an antineutrino. Understanding these principles lays the foundation for accurately predicting the products of beta minus decay and writing balanced nuclear equations that represent these transformations.

The general form of a nuclear equation is:

Parent Nucleus β†’ Daughter Nucleus + Emitted Particles

Where:

  • The Parent Nucleus is the original radioactive nucleus.
  • The Daughter Nucleus is the nucleus formed after the decay.
  • Emitted Particles include the beta particle (Ξ²-) and the antineutrino (Ξ½Μ„e) in the case of beta minus decay.

To write a balanced nuclear equation, you need to ensure that the sum of the mass numbers (superscripts) and the sum of the atomic numbers (subscripts) are the same on both sides of the equation. This reflects the fundamental laws of conservation in nuclear reactions. Let's delve deeper into the specifics of beta minus decay and how it affects the composition of the nucleus.

Cobalt-60 and Beta Minus Decay

Cobalt-60 (Co-60) is a radioactive isotope of cobalt that is widely used in various applications, including medical treatments and industrial radiography. Understanding the decay process of Co-60 is crucial for its safe handling and utilization. Co-60 undergoes beta minus decay, transforming into another element while emitting a beta particle. In beta minus decay, a neutron within the nucleus of Co-60 converts into a proton. This conversion results in the emission of an electron (Ξ²-) and an antineutrino (Ξ½Μ„e). The beta particle, being essentially a high-energy electron, carries a charge of -1 and has a negligible mass compared to nucleons (protons and neutrons). The antineutrino is an elementary particle with no charge and very little mass, often represented as Ξ½Μ„e. This transformation within the nucleus is the core of the beta minus decay process, and it's essential to understand how it affects the composition of the atom. As the neutron transforms into a proton, the atomic number of the nucleus increases by one, leading to a change in the element. However, the total number of nucleons (protons + neutrons) remains constant, thus maintaining the same mass number. The specific details of this transformation are crucial when constructing the balanced nuclear equation for the decay of Co-60.

The key changes during beta minus decay are:

  • Atomic Number Increases by 1: Due to the conversion of a neutron into a proton.
  • Mass Number Remains the Same: As the total number of nucleons is unchanged.
  • Emission of a Beta Particle (Ξ²-): An electron emitted from the nucleus.
  • Emission of an Antineutrino (Ξ½Μ„e): A neutral, nearly massless particle.

Given these changes, we can now analyze the possible balanced nuclear equations for the beta minus decay of Co-60.

Analyzing the Proposed Nuclear Equations

To determine the correct balanced nuclear equation for the beta minus decay of Co-60, we need to examine each option provided and verify whether it adheres to the conservation laws. Let's consider the options one by one, breaking down each component and ensuring that the mass numbers and atomic numbers balance on both sides of the equation. This step-by-step analysis will allow us to identify any inconsistencies and pinpoint the equation that accurately represents the nuclear transformation. It's essential to pay close attention to the subscripts and superscripts, which denote the atomic number and mass number, respectively. These numbers provide critical information about the composition of each nucleus involved in the decay process. Furthermore, understanding the properties of the emitted particles, such as the beta particle, is crucial for correctly balancing the equation. The beta particle, with its negative charge and negligible mass, plays a significant role in the overall charge and mass balance of the nuclear reaction. By carefully evaluating each option, we can confidently determine the balanced nuclear equation that accurately describes the beta minus decay of Co-60.

Option 1: 2760Coightarrow2660Fe++10e{}_{27}^{60} Co ightarrow {}_{26}^{60} Fe + {}_{+1}^{0} e

  • Left Side: Cobalt-60 (Co-60) has an atomic number of 27 and a mass number of 60.
  • Right Side: Iron-60 (Fe-60) has an atomic number of 26 and a mass number of 60. The positron (+10e{}_{+1}^{0} e) has an atomic number of +1 and a mass number of 0.
  • Analysis: The mass numbers are balanced (60 = 60), but the atomic numbers are not (27 β‰  26 + 1). This equation incorrectly represents beta minus decay as it shows a decrease in atomic number, which is characteristic of positron emission, not beta minus decay. In beta minus decay, the atomic number should increase by one due to the conversion of a neutron into a proton within the nucleus. This fundamental difference highlights why this equation is not a valid representation of the process. Furthermore, the emitted particle is a positron, which is associated with positron emission rather than beta minus decay. Therefore, this option can be definitively ruled out as an accurate description of the beta minus decay of Co-60.

Option 2: 2760Coightarrow2860Ni+βˆ’10e{}_{27}^{60} Co ightarrow {}_{28}^{60} Ni + {}_{-1}^{0} e

  • Left Side: Cobalt-60 (Co-60) has an atomic number of 27 and a mass number of 60.
  • Right Side: Nickel-60 (Ni-60) has an atomic number of 28 and a mass number of 60. The beta particle (βˆ’10e{}_{-1}^{0} e) has an atomic number of -1 and a mass number of 0.
  • Analysis: The mass numbers are balanced (60 = 60), and the atomic numbers are also balanced (27 = 28 - 1). This equation correctly represents beta minus decay, where the atomic number increases by one due to the emission of a beta particle. The transformation of Co-60 into Ni-60 with the emission of an electron is the hallmark of beta minus decay, aligning with the fundamental principles of nuclear physics. The beta particle carries a negative charge, which balances the increase in the positive charge within the nucleus as a neutron converts into a proton. This careful balance of charge and mass is crucial for the stability of the nuclear equation and accurately reflects the observed nuclear transformation. Thus, this option appears to be the correct representation of the beta minus decay of Co-60.

Option 3: 2760Co++10e{}_{27}^{60} Co + {}_{+1}^{0} e

  • Analysis: This option is incomplete and does not represent a nuclear equation. It lacks a product side, making it impossible to determine if it represents a balanced nuclear reaction. A complete nuclear equation must show both the reactants and the products, allowing for the verification of conservation laws. The absence of products in this option renders it invalid as a representation of the beta minus decay of Co-60. Nuclear equations are fundamentally about transformations, showing how a parent nucleus changes into daughter nuclei and particles. Without the product side, there is no way to assess the transformation or determine if the equation is balanced. Therefore, this option can be immediately dismissed as it does not fulfill the basic requirements of a nuclear equation.

The Correct Balanced Nuclear Equation

After analyzing the proposed nuclear equations, it is evident that the second option correctly represents the beta minus decay of Co-60. The equation is:

2760Coightarrow2860Ni+βˆ’10e{}_{27}^{60} Co ightarrow {}_{28}^{60} Ni + {}_{-1}^{0} e

This equation accurately depicts the transformation of Cobalt-60 (Co-60) into Nickel-60 (Ni-60) with the emission of a beta particle (βˆ’10e{}_{-1}^{0} e). In this process, a neutron within the Co-60 nucleus converts into a proton, increasing the atomic number by one (from 27 to 28) while the mass number remains unchanged at 60. The emitted beta particle, which is essentially a high-energy electron, carries a charge of -1 and a negligible mass. This equation adheres to the fundamental laws of conservation, ensuring that both the mass number and the atomic number are balanced on both sides. The mass number remains constant at 60, and the sum of the atomic numbers on both sides is equal (27 = 28 - 1). Therefore, this equation provides a comprehensive and accurate representation of the beta minus decay of Co-60, capturing the essential changes that occur at the nuclear level.

Key Points That Confirm the Answer:

  • Atomic Number Increase: The atomic number increases by 1, which is characteristic of beta minus decay.
  • Mass Number Conservation: The mass number remains the same, indicating that the total number of nucleons is conserved.
  • Emission of a Beta Particle: The presence of βˆ’10e{}_{-1}^{0} e signifies the emission of a beta particle, a key feature of beta minus decay.
  • Balanced Equation: The equation is balanced in terms of both mass number and atomic number, adhering to the conservation laws.

Conclusion

In conclusion, the balanced nuclear equation that represents the beta minus decay of Co-60 is 2760Coightarrow2860Ni+βˆ’10e{}_{27}^{60} Co ightarrow {}_{28}^{60} Ni + {}_{-1}^{0} e. This equation accurately illustrates the nuclear transformation where Cobalt-60 decays into Nickel-60 by emitting a beta particle. The atomic number increases by one, reflecting the conversion of a neutron into a proton, while the mass number remains constant, indicating that the total number of nucleons is conserved. The equation is meticulously balanced, ensuring that both the mass numbers and atomic numbers are equal on both sides, thus adhering to the fundamental principles of nuclear chemistry. Understanding how to balance nuclear equations is essential for predicting the products of radioactive decay and comprehending the underlying processes involved in nuclear transformations. This knowledge is crucial not only in academic settings but also in practical applications, such as nuclear medicine, where radioactive isotopes like Co-60 are used for diagnostic and therapeutic purposes. The ability to correctly interpret and balance nuclear equations provides a solid foundation for further exploration of nuclear phenomena and their applications in various fields of science and technology. Therefore, a thorough understanding of these principles is paramount for anyone studying or working in areas related to nuclear chemistry and physics. This specific example of Co-60 decay serves as a valuable illustration of the broader concepts involved in radioactive decay and nuclear reactions.