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When two monochromatic lights of frequency, $\upsilon$ and $\upsilon/2$ are incident on a photoelectric metal, their stopping potential becomes $V_s/2$ and $V_s$ respectively. The threshold frequency for this metal is :
Detailed Solution
Using Einstein's equation $eV = h\nu - h\nu_{th}$:
$\frac{eV_s}{2} = h\nu - h\nu_{th}$ ...(1)
$eV_s = \frac{h\nu}{2} - h\nu_{th}$ ...(2)
Solving (1) and (2) gives a negative threshold frequency, which is not possible – the data given in the question is incorrect.
This question was declared a bonus.