This paper is a step in the direction of developing a computer model of the near source dispersal of suspended particulate matter (SPM) in planetary boundary layer (PBL). Since Surface Mine blasting is done during daytime, study of daytime dispersion in convective boundary layer (CBL) is relevant to the mining engineers. The scope of this paper covers dispersal after the blast in any type of PBL ie stable, convective and neutral but only under weak wind condition. Mathematical analysis of the dispersion of vertical dust column has been carried out during weak wind conditions in a tropical meteorological environment. It is noted that dust concentration reaches its maximum value some distance away from the point of blast, immediately after the blast (t*=1) and thereafter rapidly decreases. After a short interval from the time of blast at t*=11 the dust concentration shows linear decrease in concentration with distance. Dust concentration also rapidly drops during the interval t*=1 to t*=11, thereafter, rate of drop is nearly the same at any distance from the point of blast.