The kinetic energy of emitted electron is E when the light incident on the metal has wavelength λ . To double the kinetic energy, the incident light must have wavelength:

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Using Einstein's photoelectric equation, kinetic energy of an electron is $E$ when the incident wavelength is $λ$ is $E = \frac{h c}{λ} - ϕ . . . (1)$
When kinetic energy doubles, then, $2 E = \frac{h c}{λ^{'}} - ϕ . . . (2)$
Subtracting $(2) - (1)$ , we have
$E = h c (\frac{1}{λ^{'}} - \frac{1}{λ})$
$\Rightarrow λ^{'} = \frac{h c λ}{E λ + h c}$

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