Question

Is it possible to have en electromagnetic wave with a wavelength of `99.7` nm and an energy of `1.99*10^-18` J?

Answer 1

Yes.

Explanation:

Energy of an electromagnetic wave is given by

`"E" = "hc"/λ`

Here, `"c"` and `"h"` are constants.

Speed of electromagnetic wave is approximately `3 × 10^8\ "m/s"`. So, after plugging in the values of `"E"`, `"h"` and `lamda` if we get value of `"c"` approximately equal to `3 × 10^8\ "m/s"` then we can say that the wave is possible.

`"c" = "E λ"/"h" = (1.99 × 10^-18\ "J" × 99.7 × 10^-9\ "m")/(6.626 × 10^-34\ "J s") ≈ 3.0 × 10^-8\ "m/s"`

∴ The given conditions are possible for an electromagnetic wave.

Answer 2

`E=hf=(hc)/lambda` where:

• `E` = Energy (`J`)
• `h` = Planck's constant (`6.63*10^-34` `Js`)
• `c` = speed of light (`~3*10^8ms^-1`)
• `lambda` = wavelength (`m`)

`E=((6.63*10^-34)(3*10^8))/(99.7*10^-9)~~1.99*10^-18J=1.99*10^-18J`

A photon can have an energy of `1.99*10^-18J` and a wavelength of `99.7nm`