When a baby's cord stump falls depend on a few factors. Some of it is individual, but what you put on the cord stump to care for it and whether the stump is exposed to air also plays a role. Cord stumps that are wet often take a longer time to fall off. On the whole, you can expect the cord stump to fall off within a week. Caring for your baby's umbilical cord stump in the right way is important, though guidelines vary. Many new parents are advised to put alcohol or iodine on there, depending on their location. Some parents use herbal solutions or even breast milk.
There is some evidence to suggest that cord stumps that are kept dry (avoid baths in the early days) and are exposed to air a lot, fall off sooner. Putting nothing at all on the cord stump may be the best way to encourage healing, and early severing. Watch out for signs of oozing or infection whether your baby is a few days old, or already over a week old, these are signs that the healing process is not going well. Talk to your doctor if you are worried. If you are just slightly concerned, give the site lots of air and keep it dry. The situation should improve within a day, or a visit to your pediatrician is warranted. Good luck! Want to read more about newborn care? See what to do when your newborn just won't sleep.