Schlumberger Oilfield UK admitted breaching health and safety legislation following the incident on a North Sea mobile drilling rig more than 200 miles off Dundee.
Prosecutors said 14 workers from other companies had been put at risk of radiation exposure in the incident on 4 April, 2008.
The oilfield services firm pleaded guilty at Aberdeen Sheriff Court to a contravention of the Health and Safety at Work Act.
The Crown Office said Schlumberger had been contracted to carry out surveying work as part of the Maersk drilling programme for the Cawdor well.
The work at the Ensco 101 rig involved lowering into the well a scientific tool fitted with a radioactive source. However, the source was not loaded properly during preparations and it lay on the drill floor for about four hours before being spotted.
The case was investigated by the Health and Safety Executive and reported to the Crown Office and Procurator Fiscal Service (COPFS).
Following the hearing, Elaine Taylor, head of the health and safety division at the COPFS, said: "Workers who were in close proximity to the source were placed in danger as a result of failings on a range of issues, including risk assessment, the system of work, training and instruction."
Schlumberger said it had co-operated fully with the investigation and taken steps to make sure such an incident could not happen again. The firm, which employs 105,000 people worldwide, also said the maximum estimated exposure received by any of the workers had been "significantly less" than the statutory limit.