Question

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

Answer 1

Answer:

The number of photons are $5.028\times 10^{27}$.

Explanation:

$E=\frac{h\times c}{\lambda}$

where,

E = energy of photon =  

h = Planck's constant = $6.63\times 10^{-34}Js$

c = speed of light = $3\times 10^8m/s$

$\lambda$ = wavelength = 10.0 μm  =$10^{-5} m$

1 μm = $10^{-6} m$

$E=\frac{6.63\times 10^{-34}Js\times 3\times 10^8m/s}{10^{-5} m}$

$E=1.989\times 10^{-20} Joules$

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

$n\times E=E'$

$n\times 1.989\times 10^{-20} J=1000 J$

$n=\frac{1000 J}{1.989\times 10^{-20} J}=5.028\times 10^{27}$

The number of photons are $5.028\times 10^{27}$.

Answer 2

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