Question

humans are warned to shield their eyes from ultraviolet radiation with wavelengths shorter than 300 nm but not from infrared radiation with wavelengths of about 900 nm. which of the following explains the reason for this based on what happens at the molecular level with exposure to these types of radiation?
a 900 nm radiation has triple the energy of 300 nm radiation, so infrared radiation is more likely to promote electrons or break covalent bonds.
b 900 nm radiation has one - third the energy of 300 nm radiation, so infrared radiation is more likely to cause molecular rotation to occur.
c 300 nm radiation has triple the energy of 900 nm radiation, so ultraviolet radiation is more likely to promote electrons or break covalent bonds.
d 300 nm radiation has one - third the energy of 900 nm radiation, so ultraviolet radiation is more likely to cause molecular vibration to occur

Explanation:

Step1: Recall the energy - wavelength relationship

The energy of a photon is given by the formula \(E=\frac{hc}{\lambda}\), where \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength.

Step2: Calculate the energy ratio

Let \(\lambda_1 = 300\space nm\) and \(\lambda_2=900\space nm\). Then \(E_1=\frac{hc}{\lambda_1}\) and \(E_2 = \frac{hc}{\lambda_2}\). The ratio \(\frac{E_1}{E_2}=\frac{\lambda_2}{\lambda_1}\). Substituting the values, \(\frac{E_1}{E_2}=\frac{900}{300}=3\), so \(E_1 = 3E_2\) (i.e., 300 nm radiation has triple the energy of 900 nm radiation).

Step3: Relate energy to molecular effects

Higher - energy ultraviolet radiation (\(\lambda = 300\space nm\)) has enough energy to promote electrons (e.g., in electronic transitions) or break covalent bonds. Infrared radiation (\(\lambda=900\space nm\)) has lower energy and is more associated with molecular vibrations and rotations. But the key here is the energy comparison. Since \(E\propto\frac{1}{\lambda}\), and 300 nm radiation has higher energy (triple that of 900 nm radiation), it is more likely to have more energetic effects like electron promotion or bond - breaking.

Answer:

C. 300 nm radiation has triple the energy of 900 nm radiation, so ultraviolet radiation is more likely to promote electrons or break covalent bonds