Zakah on gold jewelry

1. We have jewelry equivalent to Saudi Riyals 200,000.
2. The amount of gold is about one kilogram. The intention has always been for my wife's use and never to sell any of it. Do we have to pay Zakah? Who is supposed to pay the Zakah, my wife or me, the husband? If my wife has no income, can she sell some of the gold to pay the Zakah? How do we calculate the Zakah? Is it one time per life?

Praise be to Allah, the Lord of the World; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Ornaments and jewels such as pearls and corals and the like are not subject to Zakah, since they are just used by women for beautification and they are not likely to increase by passing time.
Allah Says (interpretation of meaning): {… and that you bring forth out of it ornaments to wear. …}[16: 14].
There is a consensus of opinion among Muslim scholars concerning the above-mentioned point as long as the quantity of such ornaments does not extend the normal standard in society.
As for Zakah of gold and silver, please read the Fatawa:
83665 and 82925.
Allah knows best.