Chandra sources: photon energy, intensity and ionisation challenge

A telescope detects X-rays in a lower-frequency band and a higher-frequency band. Both travel through a vacuum. Compare the energy per photon and the wavelength in the lower-frequency band with those in the higher-frequency band. Explain each comparison using a relevant relationship.

An isolated hydrogen atom is initially in its ground state. Removing its electron requires $13.6\mathrm{eV}$. It absorbs one ultraviolet photon with energy $20.0\mathrm{eV}$. Explain why ionisation is possible. Calculate the kinetic energy of the released electron in eV, ignoring recoil of the remaining ion. State the charge left on that ion.

A different ultraviolet beam has photons of energy $10.0\mathrm{eV}$. It passes through a dilute gas of hydrogen atoms initially in their ground state. The beam's intensity is increased while its frequency stays the same. A pupil says that the extra intensity will let a single photon ionise a ground-state hydrogen atom. Explain why this is wrong. Consider only single-photon absorption. Ignore heating, collisions, prior excitation and multiphoton processes.