Question

What is the energy of an emitted flame with a wavelength of `6.5 * 10^-20` m?

Answer 1

`3.058xx10^(-6)j`

Explanation:

we know that,
`E=hf`

`or,E=hc/lambda`[as, `c=flambda`, so, `f=c/lambda`]

`=6.626xx10^(-34)*(3*10^8)/(6.5*10^-20)`[`h`=plunk's constant, `c`= speed of light]

`=3.058xx10^(-6)j`

Answer 2

The wavelength is incredibly short!!! It is difficult to imagine how did they measure it!

Explanation:

Here you have a flame of quite short wavelength well beyond the gamma ray range!!!
If you want, I think, you could use Einstein's equation for the energy `E` of a photon of a certain frequency `nu`:
`E=h*nu`
where:
`k=6.63xx10^-34Js` is Planck's constant;
and also frequecy is related to eavelength `lambda` through the speed of light `c` as:
`c=lambda*nu`
giving an energy of:
`E=6.63xx10^-34*(3xx10^8)/(6.5xx10^-20)=3.06xx10^-6J` and this is for a photon only!!!