Which isotopic ratio needs to be determined when the age of ancient wooden objects is
investigated?
(1) U-235 to U-238 (3) N-16 to N-14
(2) H-2 to H-3
(4) C-14 to 6-12

The age of ancient wooden objects is  investigated using the C-14 to C-12.

Carbon dating provides an effective way to determine the age of a sample. The idea here is that all living organisms give out C-14 while they are alive and the amount of the isotope in a living sample is known.

The age of a sample is obtained by comparing the level of the C-14 isotope present in it to the amount present in a living tissue. Hence, the age of ancient wooden objects is  investigated using the C-14 to C-12.

Learn more about carbon dating:link

(4) C-14 to 6-12

Explanation:

Carbon dating is used to estimate the age of wooden trees which use carbon dioxide. Carbon has three naturally occurring isotopes.C-12 and C-13 are stable but C-14 is radioactive. C-14 decays to nitrogen-14 and has a half-life of 5,730 years.

Wooden trees naturally incorporate both the C-12 and C-14 during their lifetimes. When wooden trees die, it stops consuming more of radioactive carbon while the C-14 which is already present in them continues to decay back into nitrogen. With the help of C-12 to C-14 ratio, we can estimate the age of wooden objects.

d.) the average kinetic energy of the gas particles is greater in container b because its particles move faster.