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Question #44190

Difficulty: 8/10 | 🟢 Free

The Question

A sample of $H_2(g)$ at $298\text{ K}$ is irradiated with vacuum ultraviolet (VUV) light. The process involves a single-photon absorption that simultaneously dissociates the $H_2$ molecule and photoionizes one of the resulting hydrogen atoms, leaving the other atom in its ground state. Given the bond dissociation enthalpy of $H_2(g)$ is $436\text{ kJ mol}^{-1}$ and the ionization energy of $H(g)$ is $13.6\text{ eV}$ , calculate the maximum wavelength (threshold wavelength) of the incident photon required for this process. (Use $hc = 1240\text{ eV nm}$ and $1\text{ eV/molecule} = 96.5\text{ kJ mol}^{-1}$ )

Options

A.
68.4 nm
B.
78.2 nm
C.
91.2 nm
D.
274.3 nm

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Mechanism_Trap

Don't get tricked by the process! Learn the mechanical traps used in competitive exam questions.

Concepts Behind This Question

Photoelectric Effect Threshold|Bond Enthalpy Pitfall|Standard State Conditions

Why This Question Is Tricky

Common Mistakes

This problem tests the 'Bond Enthalpy Pitfall' in the context of gas-phase photochemistry.

Students frequently conflate the thermodynamic bond dissociation energy with the quantum mechanical photoelectric threshold.

The primary trap is assuming the photon only needs to overcome the ionization energy of the atom ( $91.2\text{ nm}$ distractor), ignoring the molecular binding energy that must be overcome first.

Another common error is dividing the bond energy by 2 ( $78.2\text{ nm}$ distractor), incorrectly assuming the photon only needs to supply 'half' the bond energy to free one atom for ionization.

The Franck-Condon principle dictates that the vertical transition must encompass the total energy change of the entire molecular system.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Structure of Atom - Class 11 Part 1
Concept	Photoelectric Effect Threshold
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free