Write balanced nuclear equations for the following processes. (a) Beta emission of 157Eu

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Identify the type of nuclear decay: Beta emission involves the conversion of a neutron into a proton, with the emission of a beta particle (an electron) and an antineutrino.

Write the initial nuclide: The given nuclide is Europium-157, represented as \( ^{157}_{63}\text{Eu} \).

Determine the change in atomic number: In beta decay, the atomic number increases by 1 because a neutron is converted into a proton.

Write the product nuclide: The new element will have an atomic number of 64, which is Gadolinium (Gd). The mass number remains the same, so the product is \( ^{157}_{64}\text{Gd} \).

Write the balanced nuclear equation: Combine the initial nuclide, the product nuclide, and the emitted beta particle (\( ^{0}_{-1}\beta \)) to form the equation: \( ^{157}_{63}\text{Eu} \rightarrow ^{157}_{64}\text{Gd} + ^{0}_{-1}\beta \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Nuclear Reactions

Nuclear reactions involve changes in an atom's nucleus and can result in the transformation of one element into another. These reactions include processes such as alpha decay, beta decay, and gamma emission. Understanding the type of nuclear reaction is crucial for writing balanced nuclear equations, as it dictates the particles involved and the resulting isotopes.

Beta Emission

Beta emission is a type of radioactive decay where a beta particle, which is an electron or positron, is emitted from an atomic nucleus. In beta minus decay, a neutron is converted into a proton, increasing the atomic number by one while the mass number remains unchanged. This process is essential for understanding how certain isotopes, like 157Eu, transform into different elements.

Balancing Nuclear Equations

Balancing nuclear equations requires ensuring that both the mass number and atomic number are conserved during the reaction. This means that the sum of the mass numbers and the sum of the atomic numbers on both sides of the equation must be equal. Properly balancing these equations is critical for accurately representing the nuclear processes and the resulting isotopes.