GATE 2021 BT – Question 35
α-amylase has $K_m=0.005$ M. The starch concentration for one-fourth of maximum hydrolysis rate (mM, two decimal places) is _______.
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Correct answer: 1.66 to 1.68
Explanation
**Michaelis-Menten equation:**
$$v=\frac{V_{max}[S]}{K_m+[S]} .$$
We want $v=\dfrac14V_{max}$:
$$\frac{[S]}{K_m+[S]}=\frac14\;\Rightarrow\;4[S]=K_m+[S]\;\Rightarrow\;3[S]=K_m .$$
**Numbers.** $K_m=0.005\text{ M}=5\text{ mM}$:
$$[S]=\frac{5}{3}=1.67\text{ mM}.$$
The starch concentration is **1.67 mM**.