$1\mathrm{.}5kg$ of rhodamine dye $(100\frac{m^2}{s})$ released suddenly from a point source is transported

by molecular diffusion in a one$-$dimensional medium. Assuming that the dye is conserved,

a$)$ Calculate the concentrations at a point $300m$ from the source for $t=5,10$ and $15$

minutes. $(10$ points$)$

b$)$ After $t=30$ minutes, calculate the concentrations at $x=0,300$ and $600m$ from the

source. $(10$ points$)$

c$)$ Assuming that the source point is $x=0,$ plot the concentration change $($concentration

profile$)$ in the range $t=7-1500$ after $t=7$ minutes with Excel. $(20$ points$)$