Airplane mode turns off all 5 radios. Cellular, WiFi, GPS, Bluetooth, and NFC. (Most of the time you can then turn back on individual radios as needed even with Airplane mode enabled). Some people are sensitive to electromagnetic radiation at the frequencies at which these radios broadcast. All but the NFC radio are broadcasting in the microwave range.
Check out this sweet diagram of the Electromagnetic radiation spectrum. From:
It’s interesting to note that the farthest away from the cell tower you are, the stronger your phone’s is blasting out radiation. When your phone is searching for service, GPS, or wifi it is broadcasting at full power. A normal cell phone’s radios are omnidirectional. It blasts radiation all directions. Also, when you are moving it has to blast at full power. You can try out these cases that say they try to direct most of the radiation out the back of your phone: pongcase.com. (I have not tested these claims, and am not affiliated)
Personally, I have my phone in Airplane mode almost all the time. I use Wifi whenever available, because often Wifi hotspots are much closer than the cell tower. That way my wifi radio is blasting less powerfully than the cellular radio would be. I also have a pong case on my Galaxy S4. I use a headset, handset, or speaker phone whenever calling. I try to make sure that the cell phone is never within 1″ of my body or anybody else when airplane mode is off.
As far as cancer is concerned, there is a Government study that just came indicating a link between cellular frequencies and increased risk of cancer. Read about it here:
Also, according to the FCC cell phone safety guidelines for testing a phone’s SAR rating. They require the phone to be at least 5mm from any body surface. SAR rating is the amount the radiation penetrates into a fake human full of water. So, anyone using a cellphone actually touching their body or less than 5mm away. Is actually not using their phone according to the FCC. Because of the way the intensity of the radiation greatly diminishes with distance. (Actually the ratio is an inverse square) The SAR rating when actually touching your skin could be WAY higher then the legal limit of 1.60.
A little about SAR ratings and the deplorable state of any enforceable regulations.
How to check your phones specific SAR rating:
A little about microwaves from:
Microwaves are a form of electromagnetic radiation with wavelengths ranging from one meter to one millimeter; with frequencies between 300 MHz (100 cm) and 300 GHz (0.1 cm). This broad definition includes both UHF and EHF(millimeter waves), and various sources use different boundaries. In all cases, microwave includes the entire SHF band (3 to 30 GHz, or 10 to 1 cm) at minimum, with RF engineering often restricting the range between 1 and 100 GHz (300 and 3 mm).
Bluetooth and Wifi are at 2.4GHZ, and more recently with WiFi 802.11n @ 5GHz.
In the US, cellular frequencies are 800MHz-2.5GHz
GPS is at 1175MHz-1575MHz
NFC is at 13.56 MHz