Final answer:
The question is asking for the calculation of the average effective mass of an electron that corresponds to the Fermi level of lithium (Li), which is 4.2 eV, within the Free Electron Model of Metals in physics.
Step-by-step explanation:
The question pertains to the Free Electron Model of Metals in the context of solid-state physics and asks about the effect on the Fermi energy (EF) given a specified effective mass for lithium (Li) at a Fermi level of 4.2 eV.
The Fermi energy represents the highest energy level occupied by electrons at absolute zero temperature and increases with the number of electrons in a metal because it needs to accommodate more electrons with increasing number of states due to Pauli's exclusion principle.
To obtain the same result from free electron theory as with Li's Fermi level, one would need to calculate the average effective mass of the electron that corresponds to this energy within the constraints of the Free Electron Model, which is not directly provided in the excerpts.