Modify a Data Frame column with list comprehension

I have a list with about 90k strings, and a Data Frame with several columns, I'm interested in checking whether a string of the list is in column_1 and if it is assign the same value at column_2.

I can do this:

for i in range(len(my_list)):
    item = list[i]
    for j in range(len(df)):
         if item == df['column_1'][j]:
             df['column_2'][j] = item

But I would prefer to avoid the nested loops

I tried this

for item in my list:
    if item in list(df['column _1']):
          position = df[df['column_1']==item]].index.values[0]
          df['column_2'][position]  = item

but I think that this solution is even slower and harder to read, can this operation be done with a simple list comprehension?

Edit.

Second solution it's considerable faster, about an order of magnitude. why is that? seems that in that case it has to search twice for the mach:

here:

if item in list(df['column _1'])

and here:

possition = df[df['column_1]=='tem]].index.values[0]

Still I would prefer a simpler solution.