what is the energy of a photon with a frequency of 3.6 ×  1015  hz? planck’s constant is 6.63 ×  10–34  j•s. a. 1.8 × 10–49 j b. 2.4 × 10–19 j c. 1.8 × 10–18 j d. 2.4 × 10–18 j

1) 5.12 * 10^3 photons 
Find the energy of one photon, then determine how many photons are needed to reach the sensitivity. 
E = hf 
= (6.626 * 10^-34 Js)(5.95 * 10^19 Hz) 
= 3.94247 * 10^-14 J per photon 

(2.02 * 10^-10 J) / (3.94247 * 10^-14 J/photon) = 5123.69149 photons 

Round to three sig figs. 

2) 5.77 * 10^-17 J 
Energy of pulse = Energy per photon * number of photons 
= hfn 
= (6.626 * 10^-34 Js)(1.66 * 10^13 Hz)(5250) 
= 5.774559 * 10^-17 J 

Round to three sig figs. 

3) 4.07 * 10^8 kJ/mol 
10^12 pm = 1 m 
c = fλ 
f = c/λ 
E = hf 
= hc/λ 
= [(6.626 * 10^-34 Js)(3.00 * 10^8 m/s) / (2.94 * 10^-12 m)](1 kJ/1000 J)(6.02 * 10^23 photons/mol) 
= 40702571.4 kJ/mol 

Round to three sig figs. 

4) 9.94 * 10^-1 m 
E = hc/λ 
λ = hc / E 
= (6.626 * 10^-34 Js)(3.00 * 10^8 m/s) / (2.00 * 10^-25 J) 
= 0.9939 m 

Round to three sig figs. 

5) 9.06 * 10^3 photons 
Energy of pulse = Energy per photon * number of photons 
number of photons = Energy of pulse / Energy per photon 
= Energy of pulse / (hf) 
= (3.87 * 10^-13 J) / [(6.626 * 10^-34 Js)(6.45 * 10^16 Hz)] 
= 9055.23695 photons 

Round to three sig figs. 

6) 2.78 * 10^-15 J 
This is Problem 1, except in reverse. 
Sensitivity = minumum number of photons * energy per photon 
= (5930)(6.626 * 10^-34 Js)(7.077 * 10^14 Hz) 
= 2.78070758 × 10^-15 J