In two half lives, the activity will remain 1/4 of its initial activity.

For photon,

For proton, 

      ...(ii)

Initially a photon of energy 10.2eV collides inelastically with a hydrogen atom in ground state. For hydrogen atom,

The electron of hydrogen atom will jump to second orbit after absorbing the photon of energy 10.2 eV. The electron jumps back to its original state in less than microsecond and release a photon of energy 10.2 eV.
Another photon of energy 15 eV strikes the hydrogen atom inelastically. This energy is sufficient to knock out the electron from the atom as ionisation energy is 13.6 eV. The remaining energy of 1.4 eV is left with electron as its kinetic energy.

Note : Since electron shows wave nature, it will show the phenomenon of interference.

When speed of electron increases, λ will decrease. The distance between two consecutive fringes

As λ decreases, β also decrease.

B.E. = Δm × 931.5 MeV
= (4 × 4.0026 – 15.9994) × 931.5 = 10.24 MeV

For a nucleus to disintegr ate in two half life, the probability is 3/4 as 75% of the nuclei will disintegrate in this time.

Iodine and Yttrium are medium sized nuclei and therefore, have more binding energy per nucleon as compared to Uranium which has a big nuclei and less B.E./nucleon.
In other words, Iodine and Yttrium are more stable and therefore possess less energy and less rest mass. Also when Uranium nuclei explodes, it will convert into I and Y nuclei having kinetic energies.

The smallest frequency and largest wavelength in ultraviolet region will be for transition of electron from orbit 2 to orbit 1.

The highest frequency and smallest wavelength for infrared region will be for transition of electron from ∞ to 3rd orbit.

The cut off wavelength is given by

 ...(i)

According to de Broglie equation

From (i) and (ii),