Dual Nature of Radiation and Matter

The charge of an electron was first measured by the American physicist Robert Millikan during 1909-1913. In his experiment, oil was sprayed in very fine drops (around $$10^{-4}$$ mm in diameter) into the space between two parallel horizontal plates separated by a distance $$d$$. A potential difference $$V_{AB}$$ is maintained between the parallel plates, causing a downward electric field between them. Some of the oil drops acquire a negative charge because of frictional effects or because of ionisation of the surrounding air by X-rays or radioactivity. The drops are observed through microscope. $$\rho$$ is density of oil and $$r$$ is radius of the drop under investigation.
Read the following passage and answer the questions given at the end.
On a full solar eclipse day Mr.Y did few experiments with his friends Mr. Z and Ms.W. They took photo cells of work function 1.2 $$eV$$ ,2.4 $$eV$$ and 3.6 $$eV$$ respectively. Each of them set the photocells in open field with detector $$(pA)$$ and noted the intensities half an hour before the solar eclipse till half an hour past the eclipse. An observatory described that a streak of light was observed when the solar eclipse was in full swing. Mr. Y and his team also confirmed the streak.
A particle of mass $$m$$ moves in a potential $$U(x)$$ = $$A|x|$$, where $$A$$ is a positive constant. In a simplified picture quarks (the constituents of protons, neutrons and other particles) have a potential energy of intersection of approximately this form, where x represents the separation between a pair of quarks because $$U(x)$$ $$\rightarrow$$ as $$x$$ $$\rightarrow$$ $$\infty$$. It is not possible to separate quarks from each other. This phenomenon is called quark confinement
The electron in a $$Li^{++}$$ ion is in the $$nth$$ shell, $$n$$ being very large. One of the $$K$$-electrons in another metallic atom has been knocked out. The second metal has four orbits. Now, we take two samples - one of $$Li^{++}$$ ions and the other of the second metallic ions. Suppose the probability of electronic transition from higher to lower energy levels is directly proportional to the energy difference between the two shells. Take $$hc - 1224\space eV\space nm$$, where $$h$$ is Planck's constant and $$c$$ the velocity of light in vacuum. It is found that major electromagnetic waves emitted from the two samples are identical.

Answer the following questions
A monochromatic source of light of frequency $$\nu$$ illuminates a metallic surface and ejects photoelectrons. These photoelectrons with maximum energy are just able to ionise the hydrogen atoms in the ground state. The experiment is repeated with incident radiation of frequency $$\displaystyle \dfrac{5\nu}{6}$$ .The photoelectrons emitted in this case excite the hydrogen atoms which then emits a radiation of $$\lambda=1215{\mathring{A}}$$.