MCAT Physical : Light

Study concepts, example questions & explanations for MCAT Physical

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Example Questions

Example Question #11 : Light

The first four energy levels of a hydrogen atom have the energies given above. If a hydrogen atom is initially in the n = 2 state, photons of which of the following energies could be absorbed?

Possible Answers:

1.89, 2.55, or 10.2eV

1.89eV or 2.55eV

1.89eV or 10.2eV

10.2eV only

1.89eV only

Correct answer:

1.89eV or 2.55eV

Explanation:

Absorbing a photon would have the effect of pushing the atom into a higher energy state, in this case n = 3 or n = 4. Photons with an energy equal to the difference betweeen E2 and E3 or between E2 and E4, could be absorbed.

E3 – E2 = –1.51 – (–3.40) = 1.89eV

E4 – E2 = –0.85 – (–3.40) = 2.55eV

Example Question #3 : Photons And Photon Energy

A student wishes to run an experiment that requires photons with energy between 12.5eV and 13.0eV per photon. The light source is a hydrogen lamp. Which hydrogen electron transition would produce an appropriate photon?

Possible Answers:

Correct answer:

Explanation:

To calculate photon energy from an electron transition, we use the following equation.

 

In the formula,  is the initial energy level and  is the final energy level. is a constant for the given compound. Our first step will to find the difference described in the formula using the constant given for hydrogen and an estimate for the energy produced.

We can use guess and check to estimate the discrete values that can be used for the electron energy levels.

We find that if the initial energy level is 4 and the final energy level is 1, the value of the difference is approximately -0.94.

An electron transition from energy level 4 to energy level 1 would produce a photon in the appropriate range.

Example Question #1 : Photons And Photon Energy

In the photoelectric effect experiment, incoming photons with enough energy cause the ejection of an electron from a metal plate, proving that light carries energy. Which color of visible light would you expect to produce the fastest ejected electrons?

Possible Answers:

Orange

Red

Green

Blue

Yellow

Correct answer:

Blue

Explanation:

This question can be approached in two ways. The first way is to have a general understanding of the photoelectric effect, and its equation: , where the kinetic energy of an ejected electron is equal to difference between the energy of the incoming photon, and the work function of the metal plate. If the energy of the photon is greater than that of the work function, an electron will be emitted with a speed that is proportional that difference, thus the greater the energy of the photon, the greater the total kinetic energy, and the faster the speed of the outgoing electron.

Since wavelength is inversely proportional to energy, and because we know that blue light has a wavelength around 400nm, and red light approximately 700nm, we would expect blue light to carry the most energy and thus result in the fastest ejected electron. 

A second approach to this question is to use critical reasoning. Using the concept of energy conservation, we can predict the energy of the incoming photon will be transferred to the outgoing electron. Because we know that energy is inverse to wavelength, the lowest wavelength photon will have the most energy. Applying conservation of energy principles and the fact that energy is directly proportional to velocity, it is a good assumption to reason that the lowest wavelength photon will create the highest velocity electron. This leads to the answer of blue light.

Example Question #1 : Photons And Photon Energy

Which of the following electron transitions in a hydrogen atom would emit a photon of the lowest frequency?

Possible Answers:

Correct answer:

Explanation:

A photon is emitted if the electron goes from a higher to lower energy level, so we need a choice where the energy level, n, decreases. Also, we need to look for the transition that has the smallest energy difference, since frequency is proportional to energy (f  = E/h, where h is Planck's constant). Higher energy levels are closer together, so the highest pair of levels has the smallest difference in energy and the lowest frequency of emitted photons.

Example Question #151 : Mcat Physical Sciences

A sodium lamp emits a yellow light with a frequency of . How much energy is contained in  of photons?

Possible Answers:

Correct answer:

Explanation:

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:

Example Question #7 : Photons And Photon Energy

An incandescent light bulb is shown through a glass prism. The certain wavlength of the light is then directed into a glass cuvette containing an unknown concentration of protein. Commonly, this process is called spectroscopy and is used to determine the concentrations of DNA, RNA, and proteins in solutions. The indices of reflection of air, glass, and the solution are 1, 1.5, and 1.3, respectively.

How much energy does a photon of red light with a wavelength of 690nm traveling through the solution contain?

Possible Answers:

5.25 * 10-19J

7.43 * 10-19J

3.30 * 10-19J

2.19 * 10-19J

Correct answer:

2.19 * 10-19J

Explanation:

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.

Example Question #8 : Photons And Photon Energy

What color of visible light contains enough energy to eject an electron off of a metal with a work function of ?

Possible Answers:

Green

Red

Violet

Yellow

Orange

Correct answer:

Violet

Explanation:

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.

Example Question #1 : Electromagnetic Spectrum

You observe several stars in the distance with varying colors. Which of the following stars would have the highest surface temperature?

Possible Answers:

Red

Yellow

Violet

Blue

Correct answer:

Violet

Explanation:

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

Example Question #1 : Electromagnetic Spectrum

An incandescent light bulb is shown through a glass prism. The certain wavlength of the light is then directed into a glass cuvette containing an unknown concentration of protein. Commonly, this process is called spectroscopy and is used to determine the concentrations of DNA, RNA, and proteins in solutions. The indices of reflection of air, glass, and the solution are 1, 1.5, and 1.3, respectively.

The prism is designed to select for the color of visible light that has the longest wavelength. What color is this, and what are the expected wavelength ranges?

Possible Answers:

Red; 700nm

Green; 500nm

Blue; 600nm

Orange; 600nm

Correct answer:

Red; 700nm

Explanation:

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.

Example Question #2 : Electromagnetic Spectrum

An incandescent light bulb is shown through a glass prism. The certain wavelength of the light is then directed into a glass cuvette containing an unknown concentration of protein. Commonly, this process is called spectroscopy and is used to determine the concentrations of DNA, RNA, and proteins in solutions. The indices of reflection of air, glass, and the solution are 1, 1.5, and 1.3, respectively. 

What type of light is produced by the incandescent light bulb?

Possible Answers:

IR

Visible

Ultraviolet

Gamma

Correct answer:

Visible

Explanation:

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

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