Question

Represent graphically log₁₀ (activity/dps) versus t/s. What is its slope?

Answer 1

The equation for a decay constant (λ) is given as,

`lambda = 2.303/"t" log_10  "N"_0/"N"`    ....(i)

From equation (i),

log₁₀N = `(-lambda)/2.303 "t" + log_10"N"_0`

On comparing with y = mx + c, y = log₁₀N, m = `(-lambda)/2.303`, x = t, c = log₁₀N₀

Now, `"N" prop ((- "dN")/"dt")`

Hence, instead if log₁₀N versus t, `log_10((- "dN")/("dt"))` which is log₁₀ (activity) is plotted.

The graph of log₁₀ (activity/dps) versus t/s gives a straight line which can be represented as follows:

Thus, the slope will be `(- lambda)/2.303`.