Planck’s Constant Worksheet - MR. WILLARD'S NOTES
Planck's Constant Worksheet
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Max Planck explained that energy was transferred in chunks known as quanta, equal to h. The variable h is Planck's constant equal to 6.6262 ? 10-34 J?s and the variable represents the frequency in 1/s, s-1, or Hz
(Hertz). This equation allows the calculation of the energy of photons, given their frequency. If the wavelength
is given, the energy can be determined by first using the light equation (c = ) to find the frequency, then using
Planck's equation to calculate energy.
Problem-Solving Strategy
useful equations
Known
Unknown
c =
Frequency ()
E = h
Energy (E)
c = 3.00 ? 108 m/s
Wavelength () =
Frequency () E = h Energy (E)
E = h h = 6.63 ? 10-34 J?s 1 nm = 1 ? 10-9 m
Energy (E) =
Frequency () =
Wavelength ()
1 kJ = 1000 J
Example: Light with a wavelength of 525 nm is green. Calculate the energy in joules for a green light photon.
- First find the frequency: =
=
= v 5.71 1014 s- 1 = 5.71 x 1014 Hz
- Second find the energy E = h
E (6.6262 10 34 J s)(5.71 1014s-1) = E 3.78 10 19 J / photon
Use the equations above to answer the following questions.
1. Ultraviolet radiation has a frequency of 6.8 ? 1015 Hz. Calculate the energy, in joules, of the photon. 2. Find the energy, in joules per photon, of microwave radiation with a frequency of 7.91 ? 1010 Hz. 3. A sodium vapor lamp emits light photons with a wavelength of 5.89 ? 10-7 m. What is the energy of these
photons?
4. One of the electron transitions in a hydrogen atom produces infrared light with a wavelength of 746.4 nm. What amount of energy causes this transition?
5. Find the energy in kJ for an x-ray photon with a frequency of 2.4 ? 1018 s-1. 6. A ruby laser produces red light that has a wavelength of 500 nm. Calculate its energy in joules. 7. What is the frequency of UV light that has an energy of 2.39 ? 10-18 J? 8. What is the wavelength and frequency of photons with an energy of 1.4 ? 10-21 J? 9. What is the energy of a light that has 434 nm?
10. What is the wavelength of a light that has a frequency of 3.42 x 1011 Hz?
Equations and constants: E = hn and E = hc/l c = lf c/l = f
Planck's Equation Practice Problems
E = energy of one photon with a frequency of n c = speed of light = 3.0 x 108 m/s (meters per second) h = Planck's constant = 6.63 x 10-34 J-s l = wavelength in meters f = frequency in Hz (waves/s or 1/s or s-1) n = number of photons (energy level)
1. A photon has a frequency (n) of 2.68 x 106 Hz. Calculate its energy. Ans: E = 1.78 x 10-27 J
2. Calculate the energy (E) and wavelength (l) of a photon of light with a frequency (n)
of 6.165 x 1014 Hz.
Ans: E = 4.1 x 10-19 J
l = 4.87 x 10-7 m
3. Calculate the frequency and the energy of blue light that has a wavelength of 400 nm
(h = 6.62 x 10-34 J-s).
Ans: f = 7.5 x 1014 Hz E = 4.97 x 10-19 J
4. Calculate the wavelength and energy of light that has a frequency of 1.5 x 1015 Hz.
Ans: l = 2.0 x 10-7 m
E = 9.95 x 10-19 J
5. A photon of light has a wavelength of 0.050 cm. Calculate its energy. Ans: E = 3.98 x 10-22 J
6. Calculate the number of photons having a wavelength of 10.0 ?m required to produce 1.0 kJ of
energy.
Ans: 5.0 x 1022 photons
7. Calculate the total energy in 1.5 x 1013 photons of gamma radiation having l = 3.0 x 10-12 m. Ans: 1.0 J
8. Calculate the energy and frequency of red light having a wavelength of 6.80 x 10-5 cm.
Ans: E = 2.92 x 10-19 J
f = 4.4 x 1014 Hz
9. The wavelength of green light from a traffic signal is centered at 5.20 x 10-5 cm. Calculate the
frequency.
Ans: l = 5.77 x 1014 Hz.
10. Calculate the frequency of light that has a wavelength of 4.25 x 10-9m. Identify the type of
electromagnetic radiation.
Ans: f = 7.1 x 1016 Hz.
UV radiation
11. The wavelength of a ruby laser is 650 nm. If the power of the laser is 1.5 W, how many photons are coming out of the laser every second? Ans: n 18 4.9 ?10 photons
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