Final answer:
To balance the nuclear equation 56 25 Mn → ____ + 0 -1 e, the particle needed is an isotope of iron (Fe) with a mass number of 56 and an atomic number of 26, symbolized as 56 26 Fe. This is because the emission of a beta particle (an electron) from manganese results in an increase of the atomic number by one, leading to the creation of an iron isotope.
Step-by-step explanation:
The question asks what particle is needed to complete the nuclear equation 56 25 Mn → ____ + 0 -1 e. To maintain both mass and charge balance in a nuclear equation, the particle that completes this equation must have the same mass number as the original manganese (Mn) isotope and one more unit of atomic number to account for the loss of a negative charge due to the electron (also known as a beta particle) emission.
In this case, the manganese isotope has a mass number of 56 and an atomic number of 25. When a beta particle (an electron with a mass number of 0 and a charge of -1) is emitted, the new resulting nuclide must have a mass number of 56 to conserve mass and an atomic number of 26 (one more than the original) to conserve charge. Therefore, the element that has an atomic number of 26 is iron (Fe), making the complete nuclear equation:
56 25 Mn → 56 26 Fe + 0 -1 e,
which represents the process of electron capture.