An electron in a hydrogen atom in its ground state absorsbs twice its ionisation energy. What is the wavelength of the emitted electcron ?

The ionisation energy of hydrogen is 21. 72 x 10^-19 J

So, energy supplied to the electron is 2x 21.72 x 10^-19 J. To knock the electron out of atom, it needs 21.72 x 10^-19 J. The remaining energy of 21.72 x 10^-19J appear as kinetic energy.

K.E = 1/2 mv²   or 2 K.E = mv²   or  v = (2K.E / m)^1/2

Wave length = h / mv

Wave length = h / (2 K.E. m)¹ = 1 x 10^-19 m

Formula is    -13.6Z²/N² EV/atom

Use this to find ionisation energy (as it is equal to total energy)

Then use E= hc/λ

You will get the answer.