I'm trying to make my own home wireless security system. I will be using probably 3 AA batteries to power these devices. My problem is that I need to know if the batteries will be enough to power the devices for at least 6 months. Below are the details of all the devices I will be using:

1. Mini Nano V3.0 ATmega328P Microcontroller Board w/USB Cable For Arduino
2. Makerfire Arduino NRF24L01+ 2.4GHz Wireless RF Transceiver Module
3. uxcell MC 38 Mount Wired Door Window Sensor Magnetic Reed Switch Recessed

Below are some project requirements that might be useful:

1. For the Nano, I want to put it to sleep using delay(2000) in the loop() function. The Nano will be the one checking the window sensor.
2. I will be using a project enclosure of about 4X4 inches.

If this will not be possible maybe someone knows of other devices that use less power that will be more suitable for this project? I would prefer something easy to use like Arduino Nano with USB so I can easily program it.

EDIT: sorry but I just like to add that from the main HUB component, I would like to check the status of the window sensor if it is open/closed. This will be useful if there is an open window/door around the house when going to sleep. Thanks.