When electrons are accelerated through a potential difference, the work done on them is equal to the change in their kinetic energy. When cathode rays are stopped, they lose kinetic energy which is then converted into X-rays.
Thus, work done on cathode rays (W) =V×q=12mv2 → (1)
The energy and frequency of X-rays (any radiation) is related as E=hv. Where ′h′ is Planck's constant.
But v=cλ; ∴E=hv=hcλ → (2)
Equating (1) and (2) and solving for λ.
hcλ=V×q; λ=hcVq. Substituting h=6.6×10−34Js, we have c=3×108ms−1.
V=20×103V,q=1.6×10−19C
λ=6.6×10−34×3×10820×103×1.6×10−19=0.61875A