Bohr–hydrogen energy levels: If the ionization energy of hydrogen from the ground state equals x kJ mol⁻¹, what energy is required to excite an electron from n = 2 to n = 3? Use Eₙ ∝ −1/n² and compute ΔE between levels. Choose the correct option.

Q: Bohr–hydrogen energy levels: If the ionization energy of hydrogen from the ground state equals x kJ mol⁻¹, what energy is required to excite an electron from n = 2 to n = 3? Use Eₙ ∝ −1/n² and compute ΔE between levels. Choose the correct option.

Concept/Approach For H-atom, En = −x/n² if x is the ionization energy from n = 1 (since E1 = −x). Thus, E₂ = −x/4 and E₃ = −x/9. Step-by-step ΔE (2 → 3) = E₃ − E₂ = (−x/9) − (−x/4) = x(−1/9 + 1/4) = x(5/36). Final Answer 5x/36

Difficulty: Easy

5x/36
5x
7.2x
x/6

Correct Answer: 5x/36

Explanation:

Concept/Approach
For H-atom, E_n = −x/n² if x is the ionization energy from n = 1 (since E₁ = −x). Thus, E₂ = −x/4 and E₃ = −x/9.

Step-by-step
ΔE (2 → 3) = E₃ − E₂ = (−x/9) − (−x/4) = x(−1/9 + 1/4) = x(5/36).

Final Answer
5x/36

← Previous Question Next Question→

More Questions from Chemistry

Ore of aluminium (metallurgy): Identify the most important commercial ore of aluminium used for metal extraction. Select the widely occurring hydrated oxide ore. Choose the correct option.
Hydrogen isotopes (nuclear composition): The nucleus of a hydrogen atom (protium) consists of which particles? Consider the most abundant isotope of hydrogen. Choose the correct option.
Radioactivity (safety): Given the half-lives below, which radioactive isotope would be the most dangerous to handle (highest activity per amount)? Assume equal initial amounts; shorter half-life ⇒ greater activity. Choose the correct option.
Atomic ions (electron count): How many electrons are present in the hydrogen ion H⁺? Recall that H⁺ is a proton formed by removing electrons from neutral hydrogen. Choose the correct option.
Genetics (molecular control of heredity): The inherited traits of an organism are primarily controlled by which molecules? Identify the long-term information-storage polymer in cells. Choose the correct option.
Bohr–de Broglie relation: The number of standing de Broglie waves fitting an electron’s circular orbit equals the principal quantum number n. If the maximum magnetic quantum number is +3 (so l = 3), determine the number of waves for the lowest allowed orbit with that l. Choose the correct option.
Avogadro comparison (atoms vs. molecules): Match the number of atoms in a given silver sample to an equivalent count of molecules in another substance. 21.6 g of silver is given; use atomic weight Ag = 108 g/mol to find moles and hence number of atoms. Choose the option whose sample contains the same number of molecules as atoms in the silver sample.
Everyday chemistry (bleaching): Identify the most commonly used bleaching agent in household/industrial applications. Consider agents historically and currently used for decolorizing and disinfecting. Choose the correct option.
Metals and displacement: Which metal is commonly used to recover (displace) copper from an aqueous copper(II) sulfate solution? Use the metal activity series to decide which metal will displace Cu from CuSO₄. Choose the correct option.
Food chemistry (stimulants): Identify the principal active constituent responsible for the stimulant effect of tea and coffee. Think of the purine alkaloid found in both beverages. Choose the correct option.

Discussion & Comments

No comments yet. Be the first to comment!

Join Discussion