Query regarding range variation with frequency
Can someone explain why the range is more in the low frequency spectrum?
Also, i was checking out IC transceivers. Transceivers in the low frequency range seem to have more dBm rating than the ones in the high frequency range. For example, a CC2500 for 2.4 GHz has a max power setting of 1 dBm or CC2520 has till 5 dBm while CC1050 for 300MHz has till 12 dBm. Why is this so?
Is the performance of a PCB antenna better or chip antenna better?
Your question is not correct and answer is not so easy and straight.
In any radio (or wireless) communication link, the range depends on many important parameters ; the most important is the S/N ratio in the receiver.
Check any radio/wireless textbook for details. You need to consider transmitter output power, antenna gains, signal spectrum bandwidth, type of modulation, noise figure of the receiver, coding... even the type of terrain is important. You can communicate over the globe with a fraction of one watt at short waves by utilizing knowledge about solar activity affecting the ionospheric layers.
Learn and make experiments!
I'm not sure to correctly understand your question. However, considering a perfect line-of-sight link, the path loss (losses due to the signal travelling over the aether) is frequency dependent and the lower the frequency the longer the range.
In a simplistic way you can consider that the electric field is expressed as V/m then the longer the antenna the higher the voltage accross it. Since a lower frequency means to have the resonance with a longer wire (your antenna) then
"lower frequency" --> "longer antenna" --> "higher received (or transmitted) signal".
Real word propagation generally depends also by other factors.
The output power of the transceivers you mentioned is not relatated to the frequency itself, but probably is following the standard for which each of them has been designed.