Question

What is the energy of an electromagnetic wave that has a wavelength of 9.0 10-6 m? Use the equation , where hc = 1.99 10-25 J•m. A. 4.5 1019 J B. 1.8 10-30 J C. 1.1 10-24 J D. 2.2 10-20 J

Answer 1

The energy of the electromagnetic wave is 2.2 × 10⁻²⁰ J

D. is the correct option

Step-by-step explanation:

The energy of an electromagnetic wave can be calculated from

`E = h\\u`

Where
`h` is Planck's constant, (
`h =` 6.626 × 10⁻³⁴ m²kg/s )

`\\u` is the frequency of radiation

`\\u` is also given by

`\\u = (c)/(\lambda)`

where
`c` is the velocity of electromagnetic radiation (EMR) / speed of light

(
`c =` 3.0 × 10⁸ m/s)

and
`\lambda` is the wavelength

Hence, we can write

`E = h\\u`

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

From the question, hc = 1.99 × 10⁻²⁵ J•m

Also, the wavelength,
`\lambda =` 9.0 × 10⁻⁶ m

Hence,

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

`E = (1.99 * 10^(-25) )/(9.0 * 10^(-6) )`

∴
`E = 2.2 * 10^(-20) J`

Hence, the energy of the electromagnetic wave is 2.2 × 10⁻²⁰ J