Question

Can somebody please answer these 5 questions for me! Thank you :)

In the following problems, practice calculations involving energy, wavelength and frequency:
1) What is the frequency of green light that has a wavelength of 5.14 x 10^-7m?
2) What is the wavelength of infrared radiation with a frequency of 3.85 x 10^12 Hz?
3) What is the energy of a photon with a frequency of 7.85 x 10^14 Hz?
4) What is the energy of a photon having a wavelength of 6.08 x 10^-7 m?
5) What is the wavelength of ultraviolet radian having 2.94 x 10^-8 J of energy?

Answer 1

1. The frequency of green light that has a wavelength of the
`5.14 * 10^-^7 m \ is \ 5.83 * 10^1^4 Hz.`

2. Wavelength of infrared radiation with frequency
`3.85 * 10^1^2  Hz \ is \ 7.79 * 10^-^5  m.`

3. Energy of a photon with frequency
`7.85 * 10^1^5  is \  5.181 * 10^-^1^8  J.`

4. The energy of a photon having a wavelength of
`6.08 * 10^-^7m \ is \ 3.25 * 10^-^1^9J.`

5. Wavelength of ultraviolet radiation having
`2.94 * 10^-^8J \ is  \ 6.73 * 10^-^1^8m.`

Step-by-step explanation:

The equation connecting wavelength, frequency and speed of electromagnetic radiation is

c=ϑλ

1. λ =
`5.14 * 10^-^7m`

`c=3 * 10^8 m/s`

ϑ = c/λ =
`((3 * ^8))/((5.14 * 10^-^7)) = 5.83 * 10^1^4  Hz`

2. ϑ =
`3.85 * 10^1^2  Hz`

λ= c/ϑ
`= ( (3 * 10^8))/((3.85 * 10^1^2 )) = 7.79 * 10^-^5  m`

3. E = h ϑ

`= 6.6 * 10^-^3^4 * 7.85 * 10^1^5=5.181 * 10^-^1^8J`

4. E= hc/λ

`= ( (6.6 * 10^-^3^4 * 3 * 10^8))/( (6.08 * 10^-^7))`

`=3.25 * 10^-^1^9J`

5. E=
`2.94 * 10^-^8J`

λ= hc/E

`= ( (6.6 * 10^-^3^4) * 3 * 10^8)/((2.94 * 10^-^8))`

`=6.73 * 10^-^1^8m`