Is there a sin on a woman whose hair was completely uncovered during an MRI scan due to the lack of an alternative to cover her head?

A woman's hair is considered awrah (that which must be covered), and it is not permissible to show it to a non-mahram (definition) man unless there is an urgent necessity or compelling need, such as for medical treatment, unavoidable photography, or the absence of a female doctor. If your situation was one of necessity and no alternative was available, then there is no sin upon you. Otherwise, you have committed a sin. We hope that your regret and tears are evidence of the sincerity of your repentance, for the Prophet, peace and blessings be upon him, said: "Regret is repentance."