ELT battery life
 

for certification how long must an ELT battery last in modern aircraft.

It really depends on the manfacturer. But if you check out the manufacturer's website they should publish details on this.

But the rule of thumb is that the ELT battery should be replaced every 24 months as per FAR 91.:)

Useful life is generally accepted as 48 months, so the FAA has the stipulation to replace at half life...24 months.