# Physical Chemistry : Quantum Chemistry

## Example Questions

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### Example Question #1 : Photons And Photon Energy

Which of the following quantities is zero for photons?

Both mass and speed

Neither mass nor speed

Speed

Mass

Mass

Explanation:

Photons are fundamental particles that make up electromagnetic waves (light). The key aspect of photon is that it has very high speed and no mass; therefore, mass for photons is always zero.

### Example Question #1 : Photons And Photon Energy

Which of the following is/are the same for photons in gamma rays and in visible light?

I. frequency

II. wavelength

III. speed

III only

None of these

I only

I and II

III only

Explanation:

Electromagnetic spectrum is a spectrum of different types of light. Each type of electromagnetic wave differs from one another based on the frequency and wavelength; however, the speed of every electromagnetic wave in air is . The wave equation relates the speed of an electromagnetic to its wavelength and frequency as follows. Here, is speed of light, is wavelength, and is frequency. Since is always constant, wavelength and frequency are inversely proportional to each other. This means that if the wavelength increases the frequency decreases.

### Example Question #61 : Physical Chemistry

Photons in ultraviolet rays have a wavelength of 10nm. What is the energy of photons in radio waves?      Explanation:

To solve this question, we need to use the equation relating energy of a wave to its wavelength. Here, is the energy, is Planck’s constant, is speed of light (for us it’s always ), and is the wavelength (in meters). The energy of the ultraviolet rays is  If we look at the electromagnetic spectrum we will notice that the wavelength of radio waves is a lot higher than ultraviolet rays. Since energy is inversely proportional to wavelength we can conclude that the energy of radio waves is lower than ultraviolet's. The only answer choice with an energy lower than ultraviolet rays energy is 1.24neV.

### Example Question #1 : Quantum Chemistry

After undergoing emission a molecule is __________ stable and after undergoing absorption a molecule is __________ stable.

less . . . less

more . . . less

less . . . more

more . . . more

more . . . less

Explanation:

Emission is the process of releasing (or emitting) photons from an atom whereas absorption is the process of absorbing photons. After emission, the atom releases energy (in the form of photons) and goes to a lower energy state. In absorption, however, the atom absorbs energy and goes to a higher energy state. Recall that lower energy always means more stable; therefore, after emission, an atom or molecule goes to a more stable state whereas after absorption it goes to a less stable state.

### Example Question #2 : Quantum Chemistry

The wavelength of a particular color of red-orange light is .

What is the frequency of this color?       Explanation: , where is the speed of light, is the wavelength, and is frequency. ### Example Question #62 : Physical Chemistry

Microwave radiation falls in the wavelength region of .

What is the frequency of microwave radiation that has a wavelength of ?       Explanation: , where is the speed of light, is the wavelength, and is frequency. ### Example Question #1 : Electromagnetic Spectrum And Radiation

A researcher analyzes two types of electromagnetic waves. He observes that wave A has a higher amplitude than wave B. What can you conclude about these two waves?

The relative wavelengths and speed cannot be determined without knowledge of the medium through which the wave is traveling.

Wave B has the higher wavelength

Wave A has the higher speed

Wave A has the higher wavelength

The relative wavelengths and speed cannot be determined without knowledge of the medium through which the wave is traveling.

Explanation:

Amplitude of a wave is defined as the maximum peak of oscillation or vibration. Recall that frequency, wavelength, and speed are not dependent on the amplitude and are calculated using the wave equation: Here, is the speed of the wave (which is the speed of light for electromagnetic waves), is the frequency, and is the wavelength. Amplitude of a wave is not present in this equation and, therefore, cannot be used to determine relative values of frequency, wavelength, and speed.

### Example Question #1 : Electromagnetic Spectrum And Radiation

If a star approaches earth the electromagnetic waves from the star are perceived to have shorter wavelength whereas if a star moves away from the earth the waves have longer wavelength.

When observing through a telescope, a scientist notices that star A appears red whereas star B appears blue. Which of the following is true regarding these two stars?

The number of photons from both stars is approximately the same

Star B is approaching earth

More than one of these are true

Star A is approaching earth

Star B is approaching earth

Explanation:

The phenomenon described in this question is called redshift and blueshift. All stars emit electromagnetic waves. The perceived wavelength of these waves depends on the relative motion of the object. If an object is approaching the observer (in this case, the earth) then the apparent wavelength of emitted waves decreases whereas if the object moves away then the apparent wavelength increases. This is called the Doppler effect.

To answer this question, we need to know the relative wavelengths of blue and red light. Blue light has wavelength between whereas red light has wavelength between . The question states that star A appears red and star B appears blue. Since red has the higher wavelength, star A is going away from the earth. Similarly, since blue has a lower wavelength, star B is approaching earth.

Recall that lower wavelength means higher frequency; therefore, blue has the higher frequency.

### Example Question #1 : Quantum Chemistry

Microwave rays have a __________ wavelength and a __________ energy than ultraviolet rays.

lower . . . higher

lower . . . lower

higher . . . lower

higher . . . higher

higher . . . lower

Explanation:

To solve this question, we need to first recall the electromagnetic spectrum. Microwaves have very large wavelengths. They are found between visible light and radio waves. Ultraviolet, on the other hand, is found below visible light; therefore, ultraviolet rays have smaller wavelength than microwaves.

To solve for energy we need to use the following equation. Here, is the energy, is Planck’s constant, is speed of light, and is wavelength. Since energy is inversely proportional to wavelength, higher wavelengths will lead to lower energy. This means that microwaves will have lower energy than ultraviolet rays.

Gamma rays have the lowest wavelength and highest energy whereas radio waves typically have the highest wavelength and lowest energy.

### Example Question #1 : Nuclear, Quantum, And Molecular Chemistry

Two light sources are placed equidistant from a detector. The light from light source A is detected quicker than light from light source B. What can be concluded from these results?

Source A has a higher wavelength

Source A could produce red light whereas source B could produce blue light

The results are invalid

The number of photons per unit time is higher from source A

The results are invalid

Explanation:

The question states that there are two light sources and that both are placed equidistant from a detector. This means that any differences in detection speed is not related to the distance. The question also states that the detector picks up light from source A quicker that light from source B. This means that the speed of the light from source A is faster. Recall that light (or electromagnetic rays) can have varying wavelengths and frequencies; however, the speed of all electromagnetic rays is the same. It doesn’t matter if it is gamma rays or visible light, the speed of light in air is . The information given in this question contradicts this; therefore, these results are invalid.

We cannot determine the color of the light for the light sources because we don't have any information regarding their respective wavelength or frequency. The number of photons per unit time refers to the amplitude of the wave, which also cannot be determined from the given information.

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