A photographic film needs a minimum of 80.0 kJ/mol for exposure.The frequencies of visible light are in the range 7.5 × 10¹⁴ Hz to 4.3 × 10¹⁴ Hz. Is the radiation visible to the human eye? A) yes B) no C) More information is needed.

Question

Quizplus · Accepted Answer

The energy required for exposure is 80.0 kJ/mol, which is equivalent to 80,000 J/mol. To determine if the radiation is visible, we need to calculate the energy associated with the given frequency range using the equation $E = h\nu$, where $E$ is the energy, $h$ is Planck's constant ($6.626 \times 10^{-34} \, \text{Js}$), and $\nu$ is the frequency. The highest energy for visible light would correspond to the highest frequency given, which is $4.3 \times 10^{14} \, \text{Hz}$. Calculating the energy for this frequency: $E = (6.626 \times 10^{-34} \, \text{Js}) \times (4.3 \times 10^{14} \, \text{Hz}) = 2.849 \times 10^{-19} \, \text{J}$ per photon. To convert this to J/mol, we multiply by Avogadro's number ($6.022 \times 10^{23} \, \text{mol}^{-1}$): $2.849 \times 10^{-19} \, \text{J/photon} \times 6.022 \times 10^{23} \, \text{mol}^{-1} = 171.5 \, \text{kJ/mol}$. This energy is higher than the minimum required (80.0 kJ/mol), indicating that the highest frequency (and thus the entire range) of visible light can expose the film. However, the question asks if the radiation is visible to the human eye, not if it can expose the film. The provided frequencies are within the visible range, but the question's context about exposure energy and calculation might seem misleading. The correct interpretation based on the question's phrasing should focus on whether the frequencies fall within the visible spectrum, which they do. However, the explanation provided focuses on the energy required for exposure, which might not directly answer the question about visibility. Given the frequencies fall within the visible range, the radiation is visible. The explanation mistakenly concludes the radiation isn't visible based on the energy required for exposure, which was not the question. The correct answer, based on the visibility of the frequencies, should be "yes," but the explanation provided incorrectly justifies a "no" response.

A Photographic Film Needs a Minimum of 80