This thesis provides the measurements of 222Rn exhalation rates, 210Pb deposition rates and excess 210Pb inventories for locations in and around Ranger Uranium Mine and Jabiru located within Kakadu National Park, Australia. Radon-222 is part of the natural 238U series decay chain and the only gas to be found in the series under normal conditions. Part of the natural redistribution of 222Rn in the environment is a portion exhales from the ground and disperses into the atmosphere. Here it decays via a series of short-lived progeny, that attach themselves to aerosol particles, to the long lived isotope 210Pb (T1/2 = 22.3 y). Attached and unattached 210Pb is removed from the atmosphere through wet and dry deposition and deposited on the surface of the earth, the fraction deposited on soils is gradually transported through the soil and can create a depth profile of 210Pb. Here it decays to the stable isotope 206Pb completing the 238U series. Measurements of 222Rn exhalation rates and 210Pb deposition rates were performed over complete seasonal cycles, August 2002 - July 2003 and May 2003 - May 2004 respectively. The area is categorised as wet and dry tropics and it experiences two distinct seasonal patterns, a dry season (May-October) with little or no precipitation events and a wet season (December-March) with almost daily precipitation and monsoonal troughs. November and April are regarded as transitional months. As the natural processes of 222Rn exhalation and 210Pb deposition are heavily influenced by soil moisture and precipitation respectively, seasonal variations in the exhalation and deposition rates were expected. It was observed that 222Rn exhalation rates decreased throughout the wet season when the increase in soil moisture retarded exhalation. Lead-210 deposition peaked throughout the wet season as precipitation is the major scavenging process of this isotope from the atmosphere. Radon-222 is influenced by other parameters such as 226Ra activity concentration and distribution, soil porosity and grain size. With the removal of the influence of soil moisture during the dry season it was possible to examine the effect of these other variables in a more comprehensive manner. This resulted in categorisation of geomorphic landscapes from which the 222Rn exhalation rate to 226Ra activity concentration ratios were similar during the dry season. These results can be extended to estimate dry season 222Rn exhalation rates from tropical locations from a measurement of 226Ra activity concentration. Through modelling the 210Pb budget on local and regional scales it was observed that there is a net loss of 210Pb from the region, the majority of which occurs during the dry season. This has been attributed to the fact that 210Pb attached to aerosols is transported great distance with the prevailing trade winds created by a Hadley Circulation cell predominant during the dry season (winter) months. By including the influence of factors such as water inundation and natural 210Pb redistribution in the soil wet season budgeting of 210Pb on local and regional scales gave very good results.