Correct Answer - Option 4 : 5.756 /min
Concept:
As per Watson and Chicks law
\({N_t} = {N_o}{e^{ - K{C^n}t}}\)
Where,
K = Rate constant which depends on the type of microorganism, the type of disinfectant and temperature
n = Constant for a particular microorganism and type of disinfectant
C = Disinfectant concentration (weight/volume)
Nt = Number of microorganism present at any time ‘t’
Calculation:
Given, t = 8 min, n = 1 and C = 0.1 g/m3
∵ We know that, \({N_t} = {N_o}{e^{ - K{C^n}t}}\)
Let 'x' be the number of micro organism present initially
99% kill of micro organism implies that at time 't' 1% of micro organism are still surviving
∴ Micro organism surviving at time 't' = (1/100) x
∴ \(\frac{1}{{100}}x = x.{e^{ - K \times 0.1 \times 8}}\)
⇒ \( - K \times 0.8 = \ln \left( {\frac{1}{{100}}} \right)\)
K = 5.76 /min