Key characteristics of the strong nuclear force:

• It is the strongest fundamental force in nature (approximately 100 times stronger than electromagnetic force).
• It is strictly short-range, operating only within nuclear dimensions of a few femtometers ($r \lt 2 - 3\,\text{fm}$).
• It is charge-independent (acts equally between proton-proton, neutron-neutron, and proton-neutron pairs).
• It is predominantly attractive at nuclear distances (becoming repulsive only at extremely short separations below $\sim 0.8\,\text{fm}$ to prevent nuclear collapse).

From the energy level diagram of hydrogen atom, the transition energy $\Delta E$ for each emission is:

• Transition A (from $-0.85\,\text{eV}$ to $-1.5\,\text{eV}$):

$$\Delta E_A = -0.85 - (-1.5) = 0.65\,\text{eV}$$

• Transition B (from $-0.85\,\text{eV}$ to $-3.4\,\text{eV}$):

$$\Delta E_B = -0.85 - (-3.4) = 2.55\,\text{eV}$$

• Transition C (from $-1.5\,\text{eV}$ to $-3.4\,\text{eV}$):

$$\Delta E_C = -1.5 - (-3.4) = 1.90\,\text{eV}$$

• Transition D (from $-1.5\,\text{eV}$ to $-13.6\,\text{eV}$):

$$\Delta E_D = -1.5 - (-13.6) = 12.10\,\text{eV}$$

Comparing transition energies:

$$\Delta E_D \gt \Delta E_B \gt \Delta E_C \gt \Delta E_A$$

Since wavelength is inversely proportional to transition energy ($\lambda = \frac{hc}{\Delta E}$), the order of wavelengths is:

$$\lambda_A \gt \lambda_C \gt \lambda_B \gt \lambda_D$$

Analysis of nuclear reactions by change in mass number $\Delta A$ and atomic number $\Delta Z$:

• Reaction A: ${}^{222}_{86}\text{Rn} \longrightarrow {}^{218}_{84}\text{Po} + {}^{4}_{2}\text{He}$. Here $\Delta A = -4, \Delta Z = -2$, which represents an $\alpha$ particle emission (Matches III).
• Reaction B: ${}^{214}_{83}\text{Bi} \longrightarrow {}^{214}_{84}\text{Po} + {}^{0}_{-1}e$. Here $\Delta A = 0, \Delta Z = +1$, which represents a $\beta^-$ particle emission (Matches II).
• Reaction C: ${}^{234}_{90}\text{Th} \longrightarrow {}^{234}_{92}\text{U} + 2\,({}^{0}_{-1}e)$. Here $\Delta A = 0, \Delta Z = +2$, which corresponds to emission of $2\beta^-$ particles (Matches IV).
• Reaction D: ${}^{22}_{11}\text{Na} \longrightarrow {}^{22}_{10}\text{Ne} + {}^{0}_{+1}e$. Here $\Delta A = 0, \Delta Z = -1$, which represents a $\beta^+$ (positron) particle emission (Matches I).

Correct match: A-III, B-II, C-IV, D-I.

Evaluation of statements:

• Doping pure silicon with trivalent impurities (like Boron, Aluminium, Indium) creates excess holes, forming a p-type semiconductor (Correct statement).
• In an n-type semiconductor, doping with pentavalent impurities introduces free conduction electrons as majority carriers, whereas holes are minority carriers. Therefore, the statement claiming majority carriers are holes is incorrect (NOT correct statement).
• In a p-type semiconductor, holes are majority carriers and electrons are minority carriers (Correct statement).
• In intrinsic semiconductors, higher temperature breaks covalent bonds to generate electron-hole pairs, increasing conductivity and thus decreasing resistivity (Correct statement).