Question

Calculate thr number of photons having a wavelength of 10.0 μm required to produce 1.0 kJ of energy.

Answer 1

ok so first you need to figure out the energy of ONE photon with that wavelength. Using E=hc/lambda, you get E= 1.99 * 10^-20 J/photon. Now, how many photons do you need to add up to get to one kilojoule=1000 joules? 1000J / (1.99 * 10^-20 J/photon) = approximately 5 * 10^22 photons hope this helps

Answer 2

The number of photons are
`5.028* 10^(27)`.

Step-by-step explanation:

`E=(h* c)/(\lambda)`

where,

E = energy of photon =

h = Planck's constant =
`6.63* 10^(-34)Js`

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

`\lambda` = wavelength = 10.0 μm =
`10^(-5) m`

1 μm =
`10^(-6) m`

`E=(6.63* 10^(-34)Js* 3* 10^8m/s)/(10^(-5) m)`

`E=1.989* 10^(-20) Joules`

Let the n number of photons with energy equal to E' = 1.0 kJ = 1000 J

`n* E=E'`

`n* 1.989* 10^(-20) J=1000 J`

`n=(1000 J)/(1.989* 10^(-20) J)=5.028* 10^(27)`

The number of photons are
`5.028* 10^(27)`.