It won't harm your baby, but mobile phones can be covered in germs. Sucking or chewing on your phone could therefore lead to your baby swallowing germs and becoming ill. Besides, if you have an expensive mobile you may not want her using it as a toy or as something to mouth!
However, if you want your baby to babble down your mobile to a relative, keep it short. You may also prefer to keep her at a short distance when you're talking on your mobile.
When a mobile is being used to make or receive a call, it emits low levels of radio waves, called non-ionising electromagnetic radiation. Two studies have shown that children who are exposed to mobile phones regularly are more likely to develop behavioural problems.
However, radio waves may not be fully responsible for this. There's a possibility that if a parent used their mobile often, they may give less attention to their baby in general. If a baby or young child is deprived of the attention she needs over time, she may develop behavioural problems.
Before you start worrying, be assured that there is not enough proof that using a mobile phone directly causes behavioural problems in children.
If you use your mobile a lot around your baby, perhaps try to save longer social calls for when she's sleeping or amusing herself.