$\begin{array}{1 1}(a)\;3\times 10^{15}Hz&(b)\;4\times 10^{10}Hz\\(c)\;4\times 10^{15}Hz&(d)\;2\times 10^{15}Hz\end{array}$

$KE_1=h(V_1-V_0)$------(i)

$KE_2=h(V_2-V_0)=\large\frac{KE_1}{2}$------(i)

Dividing equations (ii) by (i) we have

$\therefore \large\frac{V_2-V_0}{V_1-V_0}=\frac{1}{2}$

$\large\frac{1.0\times 10^{16}-V_0}{1.6\times 10^{16}-V_0}=\frac{1}{2}$

$2.0\times 10^{16}-2V_0=1.6\times 10^{16}-V_0$

$V_0=4\times 10^{15}Hz$

Hence (c) is the correct answer.

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