A free particle with initial kinetic energy 9 eV and de Broglie wavelength 1 nm enters a regionof constant potential energy V0 such that the new de Broglie wavelength is now 1.5 nm. ThenV0 is(A) 5 eV (B) 6 eV (C) 13.5 eV (D) 15 eV

Dear student,

Kinetic energy of a particle with de-broglie wavelength=
Hence when de-broglie wavelenth increases from 1nm to 1.5nm, the kinetic energy decreases fromto.
Hence from conservation of energy, the difference in energy must be existing in the form of potential energy