Your implant will not necessarily fail. However, it is imperative that you do not smoke during the healing process. The studies show that in smokers the success rate of implant surgery falls to merely 50-70%. It is because of nicotine which is acting as a vasoconstrictor. It means it squeezes the blood vessels therefore reducing the blood flow, so the whole healing process is distorted. The implant might fail if you continue smoking heavily. With every cigarette you are increasing your chances of post-op complications. Your dentist should have discussed it with you before the surgery. If they hadn’t, ask them about their recommendations.
If you decided to stop smoking now, congratulations, it is a very good decision. If you do not have any abnormal pain, swelling or redness, you do not have to worry. The implant and the bone are probably healing properly. Make sure you visit your dentist at the previously arranged appointment for a check-up. The implantologist will most likely take a few new X-rays to check everything is healing correctly.
Bear in mind that smoking is not helping the healing process and can cause unwanted complications. Read about the impact of smoking on bone grafting here.