Atomic Models

Analysis of Statements:

1. Statement (A): The de Broglie wavelength (λ) is calculated using the formula:
   λ = h / mv
   Substituting the given values:
   
   λ = 6.67 × 10⁻⁷ m = 666.67 nm.
   This statement is true.
2. Statement (B): The emission of electrons in a cathode ray tube depends on the material of the cathode, as the work function and the energy required to emit electrons vary with the material.
   This statement is true.
3. Statement (C): Cathode rays are streams of electrons that start from the cathode (negative electrode) and travel towards the anode (positive electrode) in a cathode ray tube.
   This statement is true.
4. Statement (D): The electrons themselves are not affected by the nature of the gas present in the cathode ray tube. The nature of the gas may affect the fluorescence or color of the emitted light, but not the nature of the electrons.
   This statement is false.

Conclusion: The number of true statements is 2 (A and B).

The element with 55 protons is cesium (Cs), and its atomic number is Z = 55. The electronic configuration of neutral Cs is:

For the unipositive ion Cs+, it loses the single 6s electron, and the configuration becomes:

Now count the total number of s-electrons in
• contribute s-electrons.
Thus, the number of s-electrons is 10.

• Statement A: True. The reduction potential follows the order Na > Rb > Li when considering their values.
• Statement B: False. CsI is not highly soluble in water due to weak hydration enthalpy of the large Cs⁺ ion.
• Statement C: False. Lithium carbonate decomposes on heating.
• Statement D: False. Potassium dissolved in ammonia is blue in colour and paramagnetic due to solvated electrons.
• Statement E: True. Alkali metal hydrides are ionic solids due to strong electrostatic forces.

(1) B < Al
(2) In < T l
(3) Al < Ga
(4) Ga < In

Atomic Radius Trends in the Periodic Table

The atomic radius generally changes based on the position of an element in the periodic table:

Down a Group: The Atomic radius generally increases due to the addition of electron shells.

Across a Period (Left to Right): The Atomic radius generally decreases due to increasing nuclear charge.

Evaluation of Given Pairs:

B < Al: Boron (B) and Aluminum (Al) are in Group 13. Al is below B, so Al has a larger atomic radius. Correct.

In < Tl: Indium (In) and Thallium (Tl) are in Group 13. Tl is below In, so Tl has a larger atomic radius. Correct.

Al < Ga: Aluminum (Al) and Gallium (Ga) are in Group 13. Ga is below Al, so Ga has a larger atomic radius. Correct.

Ga < In: Gallium (Ga) and Indium (In) are in Group 13. In is below Ga, so In has a larger atomic radius. Correct.

Conclusion: Based on the general trends of atomic radii in the periodic table, all the evaluated orders are correct. The initial reasoning is flawed. Indium, being below Gallium in the same group, has a larger atomic radius.