Homework 1

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

Q1.1

The brightest star in a constellation is called “Alpha”. The second brightest star is called “Beta”. Rigel is the brightest star in the constellation Orion and the seventh brightest star in the night sky, but it is called the Beta. Rigel has an emission spectrum that peaks at ~145 nm. Betelgeuse has an emission spectra of ~700nm. What is the surface temperature of Betelgeuse? How does this temperature compare with Rigel?

(Left) The seventh brightest star in the night sky, Rigel. As viewed from the Rutherfurd Observatory in midnight, the picture was processed through a telescope. (CC-BY-SA 3.0 Haktarfone) (Right) The ninth brightest star in the night sky, Betelgeuse. Image from Nasa.gov

Q1.2

Electroplated palladium has a work function of 5.22 eV. What is the shortest-energy photon that can eject an electron from palladium? What is this wavelength? What region of the electromagnetic spectrum would you identify with this radiation?

Q1.3

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

1. 40 W yellow-green LED (λ = 564 nm)
2. a 1200W microwave source (λ = 1.1 cm)

Q1.4

Beryllium has a work function of 5.0 eV. Laser light with a power per unit area of 6.0 W is incident on a Beryllium sheet.

1. Electrons with a minimum kinetic energy (KE) of 0.2 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 < \(1.00 \times 10^{-10}\; J\)?

Q1.5

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 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?

Q1.6

A laser with a power output of 3.00 mW at a wavelength of 400 nm is projected onto potassium metal.

1. How many electrons per second are ejected?
2. What power is carried away by the electrons, given that the work function is 2.3 eV?

Q1.7

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 the readings cover it nicely).

Q1.8

Infrared radiation \(1.12 \times 10^4\) nm from a CO\(_{2}\) laser is absorbed by a \(266\; g\) sample of water. The entirety of energy is converted 100% into to heat. Calculate the number of photons at this wavelength required to raise the temperature of the water by \(16^{o}C\). The specific heat capacity of water is \(4.184\dfrac{J}{g^{o}C}\). (Hint: this is a classic heat of reaction calorimetry like problem).

Q1.9

How many grams of ice can be melted after the absorption of \(4.0 \times 10^{23}\) photons at 150 nm? Given that the specific heat of fusion for water is 333.55 kJ/kg at 0°C, how many water molecules will be converted from ice into water after the absorption of these photons?

Q1.10

Science says the ideal slice of toast is cooked at a temperature of 154 °C. To reach this, a toaster coil made of a nichrome (alloys of nickel, chromium, and iron) wire coil on a mica sheet is heated to about 461 °C.

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 toast cooked at the ideal temperature.
3. Does your toast glow? If so, what is the peak wavelength?

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