Hi Dear.
It's a Essential tremor most commonly in such group of age.affects the arms, hands, and head.So please don't worry..but you have more take care of him as his age wise.
Next Steps
Keep improve his life style. Avoiding food and drinks containing caffeine. Managing stress. Getting adequate amounts of rest to reduce fatigue.and you can take advice from physical or occupational therapy as well if it's really very severe with some medication like beta-blocker most commonly propranolol may be prescribed.