Question

short answer questions
visible light:
hint: (roy.....)
radiation color frequency (hz) wavelength (nm)
reds ≈4.5 x 10¹⁴ 650 - 700
oranges ≈5.0 x 10¹⁴ 600 - 650
yellows ≈5.5 x 10¹⁴ 550 - 600
greens ≈6.0 x 10¹⁴ 500 - 550
blues ≈6.5 x 10¹⁴ 450 - 500
indigos ≈7.0 x 10¹⁴ 400 - 450
violets ≈7.5 x 10¹⁴ 380 - 400

1. which of the colors above have the longest wavelengths?
2. which of the colors above have the shortest wavelengths?
3. which of the colors above have the highest frequency?
4. describe the relationship between wavelength and frequency.
5. how are frequency and energy related?
6. what is the relationship between wavelength and energy?
7. which of the colors above have the highest energy?
8. moving in the direction of higher frequency, what comes after violet on the electromagnetic spectrum?
9. moving in the direction of lower frequency, what comes after red on the electromagnetic spectrum?
10. do all colors of white light travel at the same speed?

problems: show all three steps of using a formula - show the formula, fill in the formula, & solve for the answer.

1. what is the wavelength of a green light radiation that has a frequency of 6.26 x 10¹⁴ hz?
2. what is the wavelength of an electromagnetic radiation that has a frequency of 5.0 x 10¹² hz? what kind of electromagnetic radiation is this?

Explanation:

Step1: Identify longest - wavelength color

From the table, red has the highest wavelength range (650 - 700 nm). So the answer to question 1 is red.

Step2: Identify shortest - wavelength color

Violet has the lowest wavelength range (380 - 400 nm). So the answer to question 2 is violet.

Step3: Identify highest - frequency color

Violet has the highest frequency ($7.5\times 10^{14}$ Hz). So the answer to question 3 is violet.

Step4: Describe wavelength - frequency relationship

The relationship between wavelength ($\lambda$) and frequency ($f$) is given by the formula $c = f\lambda$, where $c$ is the speed of light in a vacuum ($c= 3\times 10^{8}$ m/s). Since $c$ is constant, wavelength and frequency are inversely proportional. So the answer to question 4 is: They are inversely proportional ($c = f\lambda$, $c$ is constant).

Step5: Describe frequency - energy relationship

The energy of a photon is given by $E = hf$, where $h$ is Planck's constant ($h = 6.63\times 10^{-34}$ Js). So energy is directly proportional to frequency. The answer to question 5 is: They are directly proportional ($E = hf$).

Step6: Describe wavelength - energy relationship

Since $c = f\lambda$ and $E = hf$, we can substitute $f=\frac{c}{\lambda}$ into $E = hf$ to get $E=\frac{hc}{\lambda}$. So energy and wavelength are inversely proportional. The answer to question 6 is: They are inversely proportional ($E=\frac{hc}{\lambda}$).

Step7: Identify highest - energy color

Since energy is directly proportional to frequency and violet has the highest frequency, violet has the highest energy. The answer to question 7 is violet.

Step8: Identify post - violet radiation

Moving to higher frequencies after violet in the electromagnetic spectrum is ultraviolet radiation. The answer to question 8 is Ultraviolet radiation.

Step9: Identify post - red radiation

Moving to lower frequencies after red in the electromagnetic spectrum is infrared radiation. The answer to question 9 is Infrared radiation.

Step10: Determine speed of white - light colors

All colors of white light travel at the same speed in a vacuum, which is the speed of light $c = 3\times 10^{8}$ m/s. The answer to question 10 is Yes.

Step11: Calculate green - light wavelength

1. Show the formula: $c = f\lambda$, so $\lambda=\frac{c}{f}$
2. Fill in the formula: $c = 3\times 10^{8}$ m/s, $f = 6.26\times 10^{14}$ Hz. $\lambda=\frac{3\times 10^{8}}{6.26\times 10^{14}}$
3. Solve for the answer: $\lambda=\frac{3\times 10^{8}}{6.26\times 10^{14}}\approx4.79\times 10^{-7}$ m = 479 nm

Step12: Calculate EM - radiation wavelength and type

1. Show the formula: $\lambda=\frac{c}{f}$
2. Fill in the formula: $c = 3\times 10^{8}$ m/s, $f = 5.0\times 10^{12}$ Hz. $\lambda=\frac{3\times 10^{8}}{5.0\times 10^{12}}$
3. Solve for the answer: $\lambda=\frac{3\times 10^{8}}{5.0\times 10^{12}} = 6\times 10^{-5}$ m = 60 $\mu$m. This is infrared radiation.

Answer:

1. Red
2. Violet
3. Violet
4. They are inversely proportional ($c = f\lambda$, $c$ is constant)
5. They are directly proportional ($E = hf$)
6. They are inversely proportional ($E=\frac{hc}{\lambda}$)
7. Violet
8. Ultraviolet radiation
9. Infrared radiation
10. Yes
11. 479 nm
12. 60 $\mu$m, Infrared radiation