Homework 1

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

Q1.1

Calculate the surface temperatures of the following stars:

1. ERi40 with an emission spectrum that peaks at 4.750 um.
2. Sirius B with an emission spectrum that peaks at 410.7 nm.
3. Rigel with an emission spectrum that peaks at ~135 nm.
4. Antares with an emission spectrum that peaks at 400nm.

Q1.2

Totino's frozen pizza rolls are pretty delicious. They cooked best at 425°F. To reach this perfect temperature, a heating coil made of a nichrome (alloy of nickel, chromium, and iron) is heated to about 590°F.

1. Make a plot of the Planck's law, the Wien displacement law, and the Rayleigh-Jeans' Law for the temperature of the nichrome wire in Kelvin.
2. Make a similar plot for your Pizza cooked at the ideal temperature.
3. At this temperature, what is the peak wavelength if you consider your pizza a blackbody radiator?

For the Wien law, let \(\alpha = 8\pi h / c^3\) and \(\beta = h/k\).

 

Q1.3

Mercury has a work function of 4.5 eV. What is the shortest-energy photon that can eject an electron from mercury? What is this wavelength? What region of the electromagnetic spectrum would you identify with this radiation?

 

Q1.4

Calculate the energy per photon and the number of photons emitted per second from

1. 60 W yellow-green tungsten filament (λ = 564 nm)
2. a 1200W microwave source (λ = 1.1 cm)
3. a 9W LED bulb (λ = 550 nm)

 

Q1.5

Mercury has a work function of 4.5 eV. Laser light with a power per unit area of 6.0 W is incident on a mercury liquid layer.

1. Electrons with a minimum kinetic energy (KE) of 0.5 keV are ejected from the sheet surface. What is the wavelength of incident light?
2. Calculate the maximum number of electrons that can be ejected by a 60 minute pulse of the incident light (under constant power).
3. How many electrons will be emitted if the energy of incident light is < \(1.00 \times 10^{-10}\; J\)?

 

Q1.6

The work function of purified \(C_{60}\) is 4.59 eV.

1. Calculate the longest wavelength that will cause the photoelectric effect in pure \(C_{60}\)?
2. When ordering \(C_{60}\), the as-received material has a workfunction of 4.38 eV because of donor impurities. When impure \(C_{60}\) is exposed to 632 nm radiation, will the maximum photoelectron kinetic energy be less than or greater than that for pure \(C_{60}\) exposed to 500 nm radiation?

 

Q1.7

A laser with a power output of 3.5 mW at a wavelength of 200 nm is projected onto potassium metal.

1. How many electrons per second are ejected?
2. What power is carried away by the electrons? Look up the work function of potassium metal using available sources.

 

Q1.8

Calculate the wavelength of a visible transition in the Balmer emission series of Hydrogen gas from the n = 3 level and to the n = 2 level. (We will have just started this in class, but read ahead!).

 

Q1.9: Basic Units Review

What units are appropriate for each variable?

1. Energy
2. Wavelength
3. Frequency (\(\nu\))
4. Mass
5. Energy Density
6. Momentum
7. Power
8. Temperature
9. Density

 

Q1.10 Basic Math Review

Perform these integrals:

1. \[ \int ax^{n}dx \]
2. \[ \int \dfrac{a}{x}dx \]
3. \[ \int \sin(ax)dx \]
4. \[ \int \cos(ax)dx \]
5. \[ \int e^{ax}dx \]

Q1.11: Derivatives

Perform these derivatives

1. \[ \dfrac{du^{n}}{dx} \]
2. \[ \dfrac{de^{u}}{dx} \]
3. \[ \dfrac{d \ln x}{dx} \]
4. \[ \dfrac{d \sin x}{dx} \]
5. \[ \dfrac{d \cos x}{dx} \]