This research work presents an algorithm for extending network lifetime in multi-hop wireless sensor networks (WSN). WSNs face energy gap issues around sink nodes due to the transmission of large amounts of data through nearby sensor nodes. The limited power supply to the nodes limits the lifetime of the network, which makes energy efficiency crucial. Multi-hop communication has been proposed as an efficient strategy, but its power consumption remains a research challenge. In this study, an algorithm is developed to mitigate energy holes around the sink nodes by using a modified ultra-low-power wake-up receiver and an energy scheduling technique. Efficient power scheduling reduces the power consumption of the relay node, and when the residual power of the sensor node falls below a defined threshold, the power emitters charge the nodes to eliminate energy-hole problems. The modified wake-up receiver improves sensor sensitivity while staying within the micro-power budget. This study's simulations showed that the developed RF energy harvesting algorithm outperformed previous work, achieving a 30% improvement in average charged energy (AEC), a 0.41% improvement in average energy (AEH), an 8.39% improvement in the number of energy transmitters, an 8.59% improvement in throughput, and a 0.19 decrease in outage probability compared to the existing network lifetime enhancement of multi-hop wireless sensor networks by RF Energy Harvesting algorithm. Overall, the enhanced power efficiency technique significantly improves the performance of WSNs.