How to compare rows within the same dataframe and create a new column for similar rows

The orignal dataframe (above) is called df

I am trying to make a new colunm called new_obj_id where if rows in column B match any row of col C the new_obj_id should then have values of obj_id that match col B

This is the expected table

This is what I tried but couldn't get through:

dataframe1['new_obj_id'] = dataframe1.apply(lambda x: x['obj_id'] 
                           if x['Column_B'] in x['Column C']
                           else 'none', axis=1)

Try this:

df['new_obj_id'] = df['Column C'].map(dict(zip(df['Column B'],df['obj_id'])))

Output:

0    a2
1    r1
2    r2
3    a1