In the result of the Geiger-Marsden experiment, by which the trajectory of the $\alpha $ -particle can be calculated ?

Energy levels $A, B$ and $C$ of a certain atom correspond to increasing values of energy, i.e. $E_A < E_B < E_C$ . If $\lambda _1, \lambda _2$ and $\lambda _3$ are the wavelengths of radiations corresponding to transitions $C$ to $B, B$ to $A$ and $C$ to $A$ respectively , which of the following relations is correct ?

Consider the following statements:

$I$. All isotopes of an element have the same number of neutrons.

$II$. Only one isotope of an element can be stable and non-radioactive.

$III$. All elements have isotopes.

$IV$. All isotopes of carbon can form chemical compounds with oxygen-$16$.

Choose the correct option regarding an isotope.

The diagram below shows the lowest four energy levels for an electron in a hypothetical atom.The electron is excited to the $-1\,eV$ level of the atom and transitions to the lowest energy state by emitting only two photons. Which of the following energies could not belong to either of the photons ? .....$eV$

What was the thickness of the gold foil kept in the Geiger-Marsden scattering experiment?

If in nature there may not be an element for which the principal quantum number $n > 4,$ then the total possible number of elements will be