Final answer:
The daughter nuclide produced in the nuclear reaction of Manganese-49 is Chromium-49 (49Cr), resulting from an electron capture process where the atomic number decreases by one but the mass number remains the same.
Step-by-step explanation:
The formula for the daughter nuclide produced in the nuclear reaction of Manganese-49 (55Mn) can be determined by considering the type of decay process involved. Since the atomic number decreases by one in this reaction, it suggests that Manganese-49 undergoes electron capture. This process involves the capturing of an electron by the nucleus, thus converting a proton into a neutron and emitting an x-ray. The new nuclide formed will still have a mass number of 49 (since electron capture does not change the mass number), but the atomic number should decrease by one. Therefore, the element with the next lower atomic number after Manganese (which has atomic number 25), is Chromium (which has atomic number 24). Thus, the resulting daughter nuclide has the symbol 49Cr.
For example, observe the decay of Uranium-238, where alpha decay results in the emission of an alpha particle, comprising two protons and two neutrons. Uranium-238 decays to form Thorium-234, illustrating the loss of protons and neutrons. In the case of Manganese-49, though we are discussing a different type of decay, it helps to understand that nuclear reactions always conserve mass number and charge.
To write a balanced nuclear equation for 55Mn undergoing electron capture:
55Mn + 0−e → 55Cr + x-ray
where 0−e represents the electron being captured.