Hello Hannah,I can’t see your ring. But let’s assume you’ll need it to be rhodium plated after the soldering or laser welding is done. This would need to be done since you have white gold. And white gold is rhodium plated when manufactured and that needs to be reapplied now and then as maintenance. Heat work necessitates re-application.
I’d say for costs, $30.00 for the fix and $35.00 for the rhodium plating. It is possible that it split because it is slightly too large for you. That is a frequent cause for ring splitting, as is a too-thin ring shank at the bottom.If the ring is too large have it re-sized at the time of your repair. If your ring is quite thin at the bottom and fits well then it probably needs to be re-shanked. This is my blog post about re-shanking. I notice you are writing from the UK. These prices are in American dollars. Your Personal Jeweler,