# Homework 1

- Page ID
- 143057

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

## Q1.1

Calculate the surface temperatures of the following stars:

- Sol with an emission spectrum that peaks at ~550 nm.
- White Dwarf GD 60 with an emission spectrum that peaks at ~ 1.3um.
- Rigel with an emission spectrum that peaks at ~135 nm.
- Betelgeuse with an emission spectrum that peaks at ~740nm.

## Q1.2

California Pizza Kitchen BBQ chicken pizza tastes delicious after cooked in a toaster oven at a balmy 450°F. To reach this perfect temperature, a heating coil made of a nichrome (alloy of nickel, chromium, and iron) is heated to about 600°F.

- 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.
- Make a similar plot for your BBQ Chicken Pizza cooked at the ideal temperature.
- 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

Chemical vapor deposition grown Bismuth has a work function of 4.22 eV. What is the shortest-energy photon that can eject an electron from bismuth? 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

- 60 W yellow-green tungsten filamanet (λ = 564 nm)
- a 1200W microwave source (λ = 1.1 cm)
- a 9W LED bulb (λ = 550 nm)

## Q1.5

Manganese has a work function of 4.1 eV. Laser light with a power per unit area of 6.0 W is incident on a manganese sheet.

- Electrons with a minimum kinetic energy (KE) of 0.2 keV are ejected from the sheet surface. What is the wavelength of incident light?
- Calculate the maximum number of electrons that can be ejected by a 60 minute pulse of the incident light (under constant power).
- 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.

- Calculate the longest wavelength that will cause the photoelectric effect in pure \(C_{60}\)?
- 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 500 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 3.85 mW at a wavelength of 350 nm is projected onto potassium metal.

- How many electrons per second are ejected?
- 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?

- Energy
- Wavelength
- Frequency (\(\nu\))
- Mass
- Energy Density
- Momentum
- Power
- Temperature
- Density

## Q1.10 Basic Math Review

Perform these integrals:

- \[ \int ax^{n}dx \]
- \[ \int \dfrac{a}{x}dx \]
- \[ \int \sin(ax)dx \]
- \[ \int \cos(ax)dx \]
- \[ \int e^{ax}dx \]

## Q1.11: Derivatives

Perform these derivatives

- \[ \dfrac{du^{n}}{dx} \]
- \[ \dfrac{de^{u}}{dx} \]
- \[ \dfrac{d \ln x}{dx} \]
- \[ \dfrac{d \sin x}{dx} \]
- \[ \dfrac{d \cos x}{dx} \]