You can create the list of dictionaries, and then use https://docs.python.org/3/library/json.html#json.dump to write it into the file

import json

f_name= 'first name'
l_name= 'last name'

#Create the list of dictionary
result = [{'f_name': f_name, 'l_name': l_name}]

import json
with open("file.json", "w") as f:
    #Write it to file
    json.dump(result, f)

The content of the json file would look like

[{"f_name": "first name", "l_name": "last name"}]

Unsurprisingly, you need the json module.

In [29]: import json

In [30]: data = '''[
    ...:    [
    ...:       1,
    ...:       "Apple"
    ...:    ],
    ...:    [
    ...:       2,
    ...:       "Orange"
    ...:    ],
    ...:    [
    ...:       3,
    ...:       "Grapes"
    ...:    ],
    ...:    [
    ...:       4,
    ...:       "Banana"
    ...:    ],
    ...:    [
    ...:       5,
    ...:       "Mango"
    ...:    ]
    ...: ]'''

In [31]: json.loads(data)
Out[31]: [[1, 'Apple'], [2, 'Orange'], [3, 'Grapes'], [4, 'Banana'], [5, 'Mango']]

The module also contains functions to handle data in files.

To extract the fruit names by numerical key could be done in several ways, but they all involve transforming the data further. For example:

In [32]: fruits = []

In [33]: for key, name in json.loads(data):
    ...:     fruits.append(name)
    ...:

In [34]: fruits[0]
Out[34]: 'Apple'

Here Python's zero-based indexing slightly defeats the value of this solution given that the keys start with 1. A dictionary gives you exactly what you need. If you call the dict constructor with a list of pairs it will treat them as key, value pairs.

In [35]: fruits = dict(json.loads(data))

In [36]: fruits[1]
Out[36]: 'Apple'

You can simply use json module with python dictionary as follow:

# Import the module
import json

# String with JSON format
data_JSON =  """
[
  {
    "id": "p01",
    "name": "Name 1",
    "price": 1,
    "quantity": 1
  },
  {
    "id": "p02",
    "name": "Name 2",
    "price": 2,
    "quantity": 2
  },
  {
    "id": "p03",
    "name": "Name 3",
    "price": 3,
    "quantity": 3
  }
]
"""

# Convert JSON string to dictionary
data_dict = json.loads(data_JSON)
print(data_dict)

To get utf8-encoded file as opposed to ascii-encoded in the accepted answer for Python 2 use:

import io, json
with io.open('data.txt', 'w', encoding='utf-8') as f:
  f.write(json.dumps(data, ensure_ascii=False))

The code is simpler in Python 3:

import json
with open('data.txt', 'w') as f:
  json.dump(data, f, ensure_ascii=False)

On Windows, the encoding='utf-8' argument to open is still necessary.

To avoid storing an encoded copy of the data in memory (result of dumps) and to output utf8-encoded bytestrings in both Python 2 and 3, use:

import json, codecs
with open('data.txt', 'wb') as f:
    json.dump(data, codecs.getwriter('utf-8')(f), ensure_ascii=False)

The codecs.getwriter call is redundant in Python 3 but required for Python 2

Readability and size:

The use of ensure_ascii=False gives better readability and smaller size:

>>> json.dumps({'price': '€10'})
'{"price": "\\u20ac10"}'
>>> json.dumps({'price': '€10'}, ensure_ascii=False)
'{"price": "€10"}'

>>> len(json.dumps({'абвгд': 1}))
37
>>> len(json.dumps({'абвгд': 1}, ensure_ascii=False).encode('utf8'))
17

Further improve readability by adding flags indent=4, sort_keys=True (as suggested by dinos66) to arguments of dump or dumps. This way you'll get a nicely indented sorted structure in the json file at the cost of a slightly larger file size.