send a test mail to investigate the point of failure.
Right click database mail –View database mail log to see error or we can SELECT * FROM msdb.dbo.sysmail_event_log ;
Check the sent_Status column in the sysmail_allitems table. The four values are sent, unsent, retrying and failed.
If the status is sent and the recipients hasn’t received the email yet, that the Database Mail external program successfully delivered the e-mail message to the SMTP server but it failed to deliver the message to the final recipient. At this point, the SMTP needs to be troubleshooted (perhaps engaged your Exchange or Mail server team)
If the status is unsent or retrying, it means that the Database Mail has not yet processed the e-mail message or is in the process of retrying after a failed attempt. This could be due to network conditions, volume of messages, SMTP server issues, etc. If the problem persists, use another profile or another mail host database.
If the status is failed, it means that the Database Mail was unable to deliver the message to the SMTP server. Check the sysmail_log table and the destination address. Also be sure that there are no Network or SMTP issues.
I work only to learn Sql Server...though my company pays me for getting their stuff done;-)