SQL Server database backup restore on lower version

No, is not possible to downgrade a database. 10.50.1600 is the SQL Server 2008 R2 version. There is absolutely no way you can restore or attach this database to the SQL Server 2008 instance you are trying to restore on (10.00.1600 is SQL Server 2008). Your only options are:

• upgrade this instance to SQL Server 2008 R2 or
• restore the backup you have on a SQL Server 2008 R2 instance, export all the data and import it on a SQL Server 2008 database.

You can use functionality called Export Data-Tier Application which generates .bacpac file consisting database schema and data.

On destination server, you can use Import Data-Tier Application option which creates and populates new database from pre-created .bacpac file

If you want just to transfer database schema, you can use Extract Data-Tier Application for creating file and Deploy Data-Tier Application for deploying created database schema.

I've tried this process on different versions of SQL Server from SQL 2014 to SQL 2012 and from SQL 2014 to SQL 2008R2 and worked well.