The Doppler broadening of gamma rays emitted during the motion of excited nuclei is measured with a high-resolution Ge(Li) detector. Results are interpreted in terms of the excited state lifetime and the processes by which the nuclei are brought to rest in condensed matter. While designed for a senior undergraduate laboratory, the experiment illustrates the principles involved in the various Doppler techniques currently used in nuclear lifetime studies and demonstrates the versatility of the Ge(Li) detector in applications other than direct energy or intensity measurement. The value55±10 fsecobtained for the lifetime of the 477-KeV state in7Liis in good agreement with values reported in the literature.