OPS 4.3 Knowledge Check

Use the momentum equation for photons: p=h/w the wavelength you found in the previous question, and Planck's constant, 6.63×10^−34, to calculate the momentum of this photon.

1.0 x 10^-27 kgm/s

Let's now multiply two numbers in scientific notation using the Google Calculator. On the Google Calculator, scientific notation is indicated by "EXP", as highlighted here: To enter scientific notation, we type in the number out in front of the multiplication symbol, then "EXP", then the number in the exponent. For example, 5×10^8 would be entered as 5, then EXP, then 8: Note in the output that 5E8 means 5×10^8. To multiply two numbers in scientific notation: (8 x 10^5)(4x10^-6) = 3.2 Now, multiply the number 4.48×10^−8 by 5.2×10^−4 using the Google Calculator. What is the correct answer in scientific notation? Note: If you are using a different calculator, the scientific notation button may be different. Sometimes it is represented by an E or EE. Ask your instructor if you are unsure!

2.33 x 10^-11

Because quantum mechanics is physics that describes the interactions of very small objects (i.e. molecules, atoms, and electrons), this week you will need to know how to multiply very small numbers. Remember that scientific notation writes very small or large number in terms of powers of 10. For example, .0008 can be written in scientific notation as 8×10−4. The exponent of 10 (-4, in this case) tells you to take the number 8.0 and move the decimal 4 places to the left giving us .0008. Which is a correct representation of .000025 in scientific notation?

2.5 x 10 ^-5

Use the energy of a photon equation: E=hf your answer from #5, and Planck's constant,6.63×10−34, to find the approximate energy of this photon:

3.0 x 10^-19 Joules

Use the frequency of light equation: f=c/w and the wavelength from Question #3 to calculate the frequency of this photon. Recall: The speed of light (c) is 3×10^8 m/s.

4.6 x 10^14 Hz

The electrons of an atom can occupy different energy shells within the atom (similar to how the planets all occupy different orbits around the Sun). Electrons prefer to be in the lowest energy shell possible (the ground state); however, they can gain energy and jump to a higher shell by absorbing light or being excited by an electric current. In accordance with the Conservation of Energy, if an electron drops from a higher energy level to a lower one, this must emit a photon (particle of light) with energy equal to the energy difference of the shells. A Balmer series transition is any transition of an electron from some higher energy shell down to the second lowest energy shell (n=2) in hydrogen. Looking at image below, what is the wavelength of a photon emitted during the Balmer transition from the n=3 shell to the n=2 shell in hydrogen?

6.56 x 10^-7 meters

Wave-particle duality tells us that wave and particle models apply to all objects whatever the size, so why don't we observe wave properties in macroscopic objects?

Because their wavelength is extremely short (undetectable).

Starting with only the Balmer series light (visible light), how could we ensure that the solar panels generate a current that Mark can use for his power station? Note: It may help to look at the electromagnetic spectrum from week 3:

By gradually increasing the frequency of the light we shine on it.

Which of the following states that all matter tends to "warp" space in its vicinity and that objects react to this warping by changing their paths?

Einstein's General Relativity

Neutron stars are:

Incredibly small remnants of supermassive stars where the gravitational collapse is halted by neutron degeneracy.

Note: The following questions are unrelated to the Balmer series or The Martian. Please refer to your course notes. A Sun-sized star will spend most of its lifetime as a:

Main-Sequence Star

If we were to illuminate them only with light from the Balmer transition considered above, would the solar panels produce a current?

No

Black holes are:

Star remnants from supermassive stars in which gravitational collapse can not be halted by electron or neutron degeneracy, and gravity is so strong in their vicinity that not even light can escape.

A glass tube is filled with hydrogen gas. An electric current is passed through the tube, and the tube begins to glow a pinkish/purple color (this is how fluorescent bulbs and neon signs produce light). If you were to pass this pink light through a prism to separate the individual light frequencies, you would see that this pink light is composed of four distinct colors: violet, green, blue, and red. Notice the similarity between image (b) below and the Balmer Series lines from Question #3. Which is the best description of why this occurs?

The electrons within the hydrogen atoms gain energy from the current causing them to jump to higher energy orbitals. When they fall back to a lower energy orbital, they release a single photon. These photons have discrete energies equal to the difference in energy of the two orbitals.

The solar panels used by Mark function because of the photoelectric effect. Light shines on the cells causing electrons to be ejected from the metal, which produces an electric current. At night on Mars, no light will fall on the solar cells and no electric current will be generated. According to your notes, what type of light is typically needed to cause the photoelectric effect?

Ultraviolet

All visible light (light that our eyes can detect) has a wavelength between 400-700 nanometers. Wavelengths just smaller than 400 nm are ultraviolet light. Wavelengths just larger than 700 nanometers are infrared light. What type of light is the Balmer series light that we have considered so far? Note: 1 nanometer = 10^−9 meters

Visible

Our Sun will eventually:

become a white dwarf star.

Imagine you are riding on a yacht in the ocean and traveling at 20 mph. You then hit a golf ball at 100 mph from the deck of the yacht. You see the ball move away from you at 100mph, while a person standing on a nearby beach would observe your golf ball traveling at 120 mph (20 mph + 100 mph). Now imagine you are aboard the Hermes spacecraft traveling at 0.1c (1/10 the speed of light) past Mars and shine a laser from the front of the ship. You would see the light traveling at c (the speed of light) away from your ship. According to Einstein's special relativity, how fast will a person on Mars observe the light to be traveling?

c (the speed of light)

A main sequence star does not expand or contract due to the balance between the internal heat pushing outward and the weight of the material pressing inward due to gravity. This state of maintaining a constant size is known as:

hydrostatic equilibrium

The lights used by Mark Watley (played by Matt Damon) during the film The Martian seem to be Metal Halide lamps. Metal Halide lamps are filled with vaporized mercury and metal-halogen compounds. When an electric current is passed through the lamp, the tube begins to glow a bright white/blue color. If you were to pass this light through a prism to separate the individual light frequencies, you would see a rainbow just as you would if using natural sunlight because of the complexity of the metal halide gas and the vast amount of possible electron transitions. Note: The study of light in this way is known as spectroscopy and allows astronomers to know exactly what atoms compose distant stars, simply by looking at the light they emit. The spectral lines an atom produces uniquely identifies that atom just like a fingerprint uniquely identifies a person. The momentum equation and energy equation that we have used above can be combined to give the following equation: c=h/p where again p is the photon momentum, E is the photon energy and c is the speed of light. When you divide the photon energy found in #6 by the photon momentum found in #4, do you get the speed of light? If not, check your wor

yes