What frequency of light would be required to excite an electron if the HOMO–LUMO energy gap was 33.9 kcal/mol (142 kJ/mol)?

검증된 단계별 안내

Step 1: Understand the relationship between energy and frequency. The energy of a photon is related to its frequency by the equation E = hν, where E is the energy, h is Planck's constant (6.626 × 10⁻³⁴ J·s), and ν is the frequency of the light.

Step 2: Convert the given energy from kcal/mol or kJ/mol to joules per molecule. Use the conversion factors: 1 kcal = 4184 J and 1 mol = 6.022 × 10²³ molecules. For example, 33.9 kcal/mol can be converted to joules per molecule by dividing the total energy in joules by Avogadro's number.

Step 3: Rearrange the equation E = hν to solve for frequency (ν). The formula becomes ν = E/h, where E is the energy in joules per molecule and h is Planck's constant.

Step 4: Substitute the calculated energy value (in joules per molecule) and Planck's constant into the equation ν = E/h to determine the frequency of light required to excite the electron.

Step 5: Ensure the frequency is expressed in appropriate units, such as hertz (Hz), which is equivalent to s⁻¹. If needed, convert the frequency to other units like THz (terahertz) for better interpretation.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

HOMO-LUMO Gap

The HOMO-LUMO gap refers to the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) in a molecule. This gap is crucial in determining the electronic properties of a compound, including its reactivity and color. A smaller gap typically indicates that a molecule can absorb lower energy light, while a larger gap requires higher energy light for electronic transitions.

Energy and Frequency Relationship

The energy of a photon is directly related to its frequency through the equation E = hν, where E is energy, h is Planck's constant, and ν (nu) is the frequency. This relationship implies that higher energy photons correspond to higher frequencies. Understanding this relationship is essential for calculating the frequency of light needed to excite an electron across the HOMO-LUMO gap.

Conversion of Energy Units

In organic chemistry, energy is often expressed in different units, such as kcal/mol or kJ/mol. To calculate the frequency of light required for an electronic transition, it is necessary to convert these energy units into joules (J). This conversion is essential for applying the energy-frequency relationship accurately, as the standard unit for energy in the equation E = hν is joules.