This paper addresses the performance analysis of Zigbee transceiver using IEEE 802.15.4 standard under 2.4 GHz frequency band in terms of Energy and Error over various fading channel conditions. Energy is a critical aspect in Wireless Sensor Network (WSN) for improved network lifetime. The multipath nature of the wireless sensor network channel imposes adverse effect on the received signal characteristics. These unreliable links increases the error level to a greater extent and hence, degrades battery life. In this paper, we investigate the energy efficiency of a Zigbee transceiver using Direct Sequence Spread Spectrum- Offset Quadrature Phase Shift Keying (DSSS-OQPSK) modulation under 2.4 GHz frequency band in a WSN. The Symbol Error Rate (SER) is computed for a Zigbee transceiver, and an expression for energy efficiency measurement is obtained. Simulation results on SER are obtained for AWGN, Rayleigh and Rician fading channels and used in energy efficiency computation. It is found that the energy efficiency of Zigbee transceivers is as low as 10% for Rayleigh channels, but it is over 90% for AWGN channels, when the received SNR is 10 dB, whereas, for Rician channels, it lies in between Rayleigh and AWGN, depending upon the fading level.