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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