Question

some instruments differentiate individual quanta of electromagnetic radiation based on their energies. Assume search and instrument has been adjusted to detect photons that have 1.00 x 10^-16 J of energy. What is the wavelength of the detected radiation? Give your answer in nanometers and in meters.

Answer 1

To find the wavelength of the detected radiation with an energy of 1.00 x 10^-16 J, we can use the relationship between energy and wavelength. The calculated wavelength is 1.9872 x 10^-7 meters or 198.72 nanometers.

Step-by-step explanation:

To calculate the wavelength of the detected radiation with an energy of 1.00 x 10-16 J, we use the equation that relates the energy (E) of a photon to its wavelength (λ):

E = h*c/λ

where:

• E is the energy of the photon,
• h is Planck's constant (6.626 x 10-34 J·s),
• c is the speed of light in a vacuum (3.00 x 108 m/s), and
• λ is the wavelength of the photon.

First, we solve for λ:

λ = h*c/E

Substituting the known values we get:

λ = (6.626 x 10-34 J·s * 3.00 x 108 m/s) / (1.00 x 10-16 J)

λ = 1.9872 x 10-7 m

To express the wavelength in nanometers (nm), we convert meters to nanometers (1 m = 109 nm):

λ = 1.9872 x 10-7 m * 109 nm/m

λ = 198.72 nm

Answer 2

1.9902 nano meter is the wavelength of the detected radiation.

Step-by-step explanation:

`E=(hc)/(\lambda)`

`\lambda` = Wavelength of radiation

E= energy of the photon of the wave

h = Planck's constant =
`6.634* 10^(-34)Js`

c = speed of light =
`3* 10^8m/s`

`\lambda = (hc)/(E)`

Energy of the radiations = E =
`1.00* 10^(-16) J`

`=(6.634* 10^(-34)Js* 3* 10^8 m/s)/(1.00* 10^(-16) J)`

`\lambda =19.902* 10^(-10)m=1.9902 nm`

`1 m = 10^9 nm`