The energy of a single photon is given by the equation:

We are given the frequency and the value of the constant, allowing us to solve.

The above gives the energy contained in one photon. Next, solve for the energy contained in  using Avogadro's number:

This question asks us about the particle nature of light and how much energy a photon would contain. From our light equations, we know that , where E is the energy of a single photon, h is Plank’s constant, and f is the frequency of the photon.

From the information in the problem, we need to determine the frequency.

We need to determine the velocity of the light in the solution. We can use the definition of index of refraction to determine this value, along with the speed of light and the index of refraction of the solution.

Now we can compute the frequency.

Substituting the frequency we found, along with Plank’s constant, we can find the energy.

Work function is the minimum amount of energy, in electron-volts, required to remove an electron from a metal surface. To calculate the energy of a single photon of light, one must use the equation:

In this formula,  is energy in Joules,  is Planck's Constant, and  is the speed of light.

To convert from Joules to eV, one must use the given conversion factor.

Use this value in the energy formula to find the wavelength of the light.

The visible spectrum spans from approximately to , with smaller wavelengths corresponding to violet and blue and larger wavelengths corresponding to red. Even without knowing the exact wavelength correlations in the spectrum, we know that our wavelength is very small and will be found in the violet end of the spectrum.

The light portion of the electromagnetic spectrum, from lowest to highest frequency, is red, orange, yellow, green, blue, indigo, violet (ROYGBIV).

Frequency is proportional to temperature, and wavelength is inversely proportional to frequency. Since the energy level corresponds with the temperature, objects that emit a higher frequency and shorter wavelength photon will have higher energy. This corresponds with violet, as it is the highest frequency (shortest wavelength) of visible light

We know that the visible spectrum has wavelengths of 390nm to 700nm. The wavelengths of light around the 700nm range are red.

Using the ROYGBIV acronym, we know that red has the longest wavelength and violet the shortest. While this may seen to be a difficult question asking for the wavelengths of light that correspond to certain colors, this is helpful on the MCAT for estimating answers and may be worth the time learning. The expected range of wavelengths for the red portion of the visible spectrum is 650nm to 700 nm. Keep in mind that, because it has the longest wavelength, red light will also have the lowest frequency.

Incandescent light bulbs produce visible light of all wavelengths. The mix of red, orange, yellow, green, blue, indigo, and violet (ROYGBIV) give the light its characteristic white appearance. For the MCAT, it is important to know the relative wavelengths of light for the visible spectrum (390 – 700nm) and where visiable wavelengths fit into the overall spectrum of electromagnetic radiation. From longest wavelength to shortest, the sequence of wavelengths is listed below.

Radio > Microwaves > Infrared > Visible > Ultraviolet > X-Rays > Gamma Rays

The highest energy of any visible light belongs to violet. The greater the wavelength, the lower the energy of the light. The greater the frequency, the higher the energy of the light. This is why ultraviolet light ("ultra" meaning "beyond" violet) is so damaging to DNA. Out of the answer choices, blue light has the lowest wavelength and greatest frequency, making it the highest energy.

The energy of a wave increases with increasing frequency and decreasing wavelength. Considering these different waves, radiowaves possess the longest wavelengths and gamma rays the shortest wavelength, thus gamma rays carry the greatest amount of energy.

Choice 5 is correct.  Highly energetic frequencies such as X-rays and gamma rays can displace electrons from materials upon which they impinge.  Microwaves are a form of radio waves, which are long-wavelength, low frequency waves with little energy. 

Mnemonic:  Microwave ovens are fundamentally safe household items.

As Einstein determined, light has properties of both a particle and a wave. In the particle sense, it has mass, velocity, and momentum. The wave property of light allows for diffraction, and constructive and destructive interference. For the MCAT, it is important to know that the photon (the particle of light) has both particle and wave properties. In fact, all objects have both particle and wave properties; however, their wave property becomes less obvious with increasing mass.