# Blackbody Radiation

## Problems

### practice

- Write something.
- Write something.
- Write something.
- Combine the speed of light (
*c*), gravitational constant (*G*), and the reduced Planck constant (ℏ) so as to generate the Planck units of…- length
- mass
- time

*k*) to the list and generate the planck unit of…- temperature

- acceleration
- force
- momentum
- energy
- power
- pressure
- density
- angular frequency

_{0}) and generate the planck units of…- charge
- current
- voltage
- resistance
- magnetic flux

### conceptual

- Pigments are used to give color to paint (on a house or on an artist's canvas), fibers (in clothing, carpeting, or tapestries), and glaze (on ceramic pottery or mosaic tiles).
- Why does red pigment appear red? Why does blue pigment appear blue?
- How does the energy of a photon of red light compare to the energy of a photon of blue light?
- Which pigment is more likely to fade first when exposed to sunlight, red or blue? Justify your answer.

- Three related questions.
- Why are ultraviolet, x-rays, and gamma rays
*always*regarded as*harmful*while infrared, microwaves, and radio waves are*generally*regarded as*benign*(by sensible people, anyway). - In what sense can visible light be thought of as "just right" as an energy source for life (and other forms of chemistry) on earth?
- Under what circumstances could exposure to the generally benign electromagnetic waves listed in part a. be considered harmful?

- Why are ultraviolet, x-rays, and gamma rays

### numerical

- A microwave oven emits 700 W of radiation at a frequency of 2.45 GHz. How many photons does it generate per second?
- The filament of a 60 W incandescent light bulb has a temperature of 3300 K.
- Assume the filament is an ideal blackbody and determine the peak wavelength of its spectrum.
- Assume the peak wavelength is equal to the mean wavelength of the visible photons emitted and determine the number of photons emitted per second.

- The world's most powerful laser is the Petawatt at Lawrence Livermore National Laboratory in California. At full energy of about 680 joules, the shots delivered by the Petawatt last a mere 440 femtoseconds. The resulting rapid dump of energy when applied to a small space is sufficient to knock neutrons loose from medium sized nuclei like gold or to split heavier nuclei like uranium in two. When applied to light nuclei like hydrogen, the power of the Petawatt could be used to initiate nuclear fusion (the process that powers the sun) in reactors on earth.
- What is the power of the Petawatt beam?
- What is the energy per photon assuming a wavelength of 1057 nm?
- How many photons are delivered per shot?

- A laser used in a fiber optic communication system operates at a wavelength of 635 nm, has a power output of 1 mW, and can transmit data at a rate of 2.5 gigabits per second. Compute the following quantities…
- the duration of a single pulse
- the length of a single pulse
- the energy of a single pulse
- the energy of a single photon
- the number of wavelengths in a single pulse
- the number of photons in a single pulse

- Complete the following table for different types of electromagnetic radiation.
energy per

photon (eV)energy per

photon (J)frequency

(Hz)wavelength

(m)type of

radiation10 ^{0}eV10 ^{3}eV10 ^{6}eV - Complete the following table for photons of visible light.
characteristic longest wavelength shortest wavelength wavelength (m) 700 nm 400 nm frequency (Hz) energy per photon (J) energy per photon (eV) color - The Balmer series is a set of wavelengths emitted by excited hydrogen atoms. Complete the following table for the four visible wavelengths in the Balmer series identified by the Greek letters α (alpha), β (beta), γ (gamma), and δ (delta).
characteristic α β γ δ wavelength (nm) 656 nm 486 nm 434 nm 410 nm frequency (Hz) energy per photon (J) energy per photon (eV) color - Photosynthesis is the process used by plants, algae, and some bacteria to convert light energy into chemical energy. A counterintuitive feature of photosynthesis is that the primary pigments involved absorb light on either side of the central part of the spectrum (typically red and blue photons) and reflect light near the center of the spectrum (green photons). Some pigments from three diverse photosynthetic systems are given in the table below. Each has two peak wavelengths around which photons are most often absorbed and used to do work. Determine the corresponding frequencies, photon energies, and color (if visible) or spectral band (infrared or ultraviolet).
Absorption peaks of some photosynthetic pigments Chl a/b: Chlorophyll a and b are found in green plants. LH2: The light harvesting complex of purple bacteria. BCHl a/b: Bacteriochlorophyll a and b are found in green sulfur bacteria. Source: Arp, et al, 2020 pigment peak λ (nm) *f*(THz)*E*(J)*E*(eV)color Chl a shorter 428 Chl a longer 660 Chl b shorter 440 Chl b longer 652 LH2 shorter 801 LH2 longer 857 BChl c shorter 431 BChl c longer 740 BChl e shorter 461 BChl e longer 655

### statistical

- led.txt

Four physics students measured the voltage drop across a batch of light emitting diodes (LEDs) connected to a simple circuit. They used a spectrometer to measure the peak wavelength of the light emitted from each LED.- Calculate the frequency (
*f*) corresponding to the peak wavelength for each LED in hertz (Hz). - Calculate the energy loss (
*E*) of the electrons flowing through the LEDs in joules (J). - Construct a graph of energy vs. frequency. Add a best fit straight line to the graph.
- Determine the value of Planck's constant (
*h*) in joule seconds (Js).

- Calculate the frequency (
- led.txt

Four physics students measured the voltage drop across a batch of light emitting diodes (LEDs) connected to a simple circuit. They used a spectrometer to measure the peak wavelength of the light emitted from each LED.- Calculate the inverse peak wavelength (λ
^{−1}) for each LED in inverse nanometers (nm^{−1}). - Calculate the energy loss (
*E*) of the electrons flowing through the LEDs in electronvolts (eV). - Construct a graph of energy vs. inverse wavelength. Add a best fit straight line to the graph.
- Determine the value of Planck's constant times the speed of light (
*hc*) in electron volt nanometers (eV nm).

- Calculate the inverse peak wavelength (λ