It is narrated from Hazrat Aisha that the right hand of the Prophet (peace be upon him) was for eating and for remembrance (of Allah), and the left hand was for other tasks.
Hadith Referenceمسند احمد / مسند النساء / 26285
Hadith Gradingحکم دارالسلام:حديث حسن بطرقه وشاهده، وهو مكرر ما قبله