Frequency and Energy Problems

E = hn      h= 6.626 x 10^-34 J/Hz          1Hz = 1/s

1)  What is the energy of a photon whose frequency is 3.0 X 10¹² Hz?

      E = hn
     E = [6.626 x 10^-34 J][3.0 X 10¹² Hz] 
             [                   Hz]
      E =[6.626 x 3.0] ^{10 (-34+12)} J
      E = 1.9 x 10^-22  J

2)  Calculate n for a l = 700 nm. n = c/l nm = nanometers
     Calculate n for a l = 400 nm. n = c/l nm = nanometers
     Calculate the energy for each wavelength.
     Which wavelength has the greatest frequency? Which wavelength has more energy?

      l = c/n   c= 3.00 X 10⁸ m/s
      Red
     n = c/l
      n = [3.00 X 10⁸ m][10⁹ nm]             
             [                  s ][  1 m   ][700 nm]
      n = [3.00/700]^{10 (8+9)} /s
      n = 4.3 x 10¹⁴ /s    or  4.3 x 10¹⁴ Hz

      Blue
      n = c/l
      n = [3.00 X 10⁸ m][10⁹ nm]             
             [                  s ][  1 m   ][400 nm]
      n = [3.00/400]^{10 (8+9)} /s
      n = 7.5 x 10¹⁴ /s    or  7.5 x 10¹⁴ Hz

      E = hn
     Red
     E = [6.626 x 10^-34 J][4.3 x 10¹⁴ Hz] 
             [                   Hz]
      E =[6.626 x 4.3] ^{10 (-34+14)} J
      E = 2.8 x 10^-19  J

      E = hn
     Blue
     E = [6.626 x 10^-34 J][7.5 x 10¹⁴ Hz] 
             [                   Hz]
      E =[6.626 x 7.5] ^{10 (-34+14)} J
      E = 5.0 x 10^-19  J

      Blue, 400 nm, has the greatest frequency and the greatest energy.

3)  A red light has a wavelength of 728 nm. 
     What is the frequency of the light?
     What is the speed of the wave in m/s?

      n = c/l
      n = [3.00 X 10⁸ m][10⁹ nm]             
             [                  s ][  1 m   ][728 nm]
      n = [3.00/728]^{10 (8+9)} /s
      n = 4.12 x 10¹⁴ /s    or  4.12 x 10¹⁴ Hz

      speed = wavelength x frequency
      speed = [728 nm][   1m    ][4.12 x 10¹⁴ /s]
                                  [10⁹ nm]
      speed = [728 x 4.12] ^10(14-9)  m/s
      speed = 2.99 x 10⁸ m/s

4) A purple light has a frequency of 7.42 x 10¹⁴ Hz. 
    What is its wavelength in nm?
    What is the energy of one quanta of light.

      l = c/n   c= 3.00 X 10⁸ m/s
      l = [3.00 X 10⁸ m][              s  ][10⁹ nm]
             [                   s][7.42 x 10¹⁴][  1m    ]
      l = [3.00/7.42] ^{10(8+ 9 - 14)}
        l = 404 nm

      E = hn
     E = [6.626 x 10^-34 J][7.42 x 10¹⁴ Hz] 
             [                   Hz]
      E =[6.626 x 7.42] ^{10 (-34+14)} J
      E = 4.91 x 10^-19  J

5) You broke your big toe!  The x ray they take of  toe uses waves that have a length 2.19 x 10¹⁰m.
     What is the speed of the wave in m/s?
     What is the wavelength in nm?
      What is the frequency of the x ray?

      n = c/l
      n = [3.00 X 10⁸ m]            
             [                  s ][2.19 x 10¹⁰ m]
      n = [3.00/2.19]^{10 (8-10)} /s
      n = 1.37 x 10^-2 /s    or  1.37 x 10^-2 Hz

      speed = wavelength x frequency
      speed = [2.19 x 10¹⁰ m ][1.37 x 10^-2 ]
                                             [                s]
      speed = [2.19 x 1.37] ^10(10+(-2))  m/s
      speed = 3.0003 x 10⁸ m/s

      l = c/n   c= 3.00 X 10⁸ m/s
      l = [3.00 X 10⁸ m][              s  ][10⁹ nm]
             [                   s][7.42 x 10¹⁴][  1m    ]
      l = [3.00/7.42] ^{10(8+ 9 - 14)}
        l = 404 nm