A typical chest X-Ray is equivalent to the normal level of background radiation received from the earth over three days

Below are some further interesting dose comparisons and the associated risks -

Note: X-Rays do not make a patient radioactive.

References:

https://www.gov.uk/government/publications/ionising-radiation-dose-comparisons/ionising-radiation-dose-comparisons
https://www.gov.uk/government/publications/medical-radiation-patient-doses/patient-dose-information-guidance

PHE Ionising Radiation Exposure of the UK population: 2010 Review