# Effective mass question

## Homework Statement

Calculate the effective mass for a free electron.

## The Attempt at a Solution

I know the above equation comes from, in the case of the free electron dispersion relation,
.

However i'm not at all sure how to go about calculating it for a free electron, given that the two formulae are basically one in the same...

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Gokul43201
Staff Emeritus
Gold Member
Note the following minor correction: the free electron dispersion relation is $\epsilon = \hbar ^2 k^2 /2m_e$. What happens when you plug this into the expression for the effective mass?