Effective mass question

[raintrek]

1. The problem statement, all variables and given/known data

Calculate the effective mass for a free electron.

2. Relevant equations

http://upload.wikimedia.org/math/4/4/f/44fe609850705ab89d76fc0714b65a4c.png

3. The attempt at a solution

I know the above equation comes from, in the case of the free electron dispersion relation, http://upload.wikimedia.org/math/1/6/3/1632e523513112a5ba15209fd3e8de9b.png.

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...

[Gokul43201]

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?