Astronomy 110 PRINT Name   __________________________ Fall 2005   Section 006 Homework 5 : Light & Atoms (Due Thursday, Oct 13, 2005)

Light

Answer question 12 on page 126 of the textbook, about the wavelengths of radio signals. Give the answers in appropriate units of length, i.e. ones that minimize the number of zeroes.

Radio waves make up part of the spectrum of light. The formula we use to determine wavelength is explained on page 91 of our text. It is:

Wavelength=speed/frequency

The problem gives us the frequency of the radio waves, so we need to know the speed. Although this formula is true for any type of wave (like ripples on a pond, or sound waves), we are talking about light waves, so we use the speed of light which is about 3*105 km/s. With a frequency of 790 kilohertz (this means that 7.9*105 waves go by you in one second):
Wavelength=(3*105 km/s)/(7.9*105 Hz)=0.38 km
A more appropriate way to write 0.38 km is in meters: 0.38 km=380 m. A radio wave with frequency 790 kHz, has a wavelength of 380 m.

For a radio wave with frequency 98.3 megahertz:
Wavelength=(3*105 km/s)/(9.83*107 Hz)=0.003 km
Again using meters for our final answer, a 9.83*107 Hz radio wave has a wavelength of 3.0 m.

Atoms

The most common atom of iron has 26 protons and 30 neutrons in its nucleus. What are its atomic number, atomic mass, and number of electrons if it is electrically neutral?

This atom has atomic number 26, atomic mass 56, and has 26 electrons.

Reason:
Atomic number is defined as how many protons an atom has. Atomic mass is a measure of how massive an atom is (measured in special units called atomic mass units) it is determined by adding the number of protons and neutrons (we can do this because protons and neutrons have about the same mass, and we ignore the electrons because their mass is much much smaller than either a proton or a neutron). Protons have positive charge, neutrons have no charge, and electrons have negative charge. In order for an atom to be neutral, all of it's charged particles have to cancel each other, so it has the same number of protons and electrons.

Consider the following three atoms: Atom 1 has 7 protons and 8 neutrons; atom 2 has 8 protons and 7 neutrons;, atom 3 3 has 8 protons and 8 neutrons. Which two are isotopes of the same element? Atom 2 and Atom 3 are the same element.

Reason:
Every element has a specific atomic number, and atomic number is determined by the number of protons, so the number of protons tells you which element it is. Atom 2 and Atom 3, both have 8 protons, while Atom 1 only has 7.

Which element is this? Oxygen

Reason:
Oxygen by definition has 8 protons in its nucleus.

Consider fluorine atoms with 9 protons and 10 neutrons. What are the atomic number and atomic mass of fluorine? Suppose we could add a proton to this fluorine nuclues. Would the result still be fluorine? No.

Reason:
As explained above, the number of protons an atom has determines which element it is. So adding a proton to Flourine makes it Neon, because Neon has 10 protons.

How many electrons could a fluorine atom lose, at most? 9 electrons.

Reason:
If we assume the Flourine atom starts out neutral then it will have 9 electrons. Taking away electrons makes Flourine positively charged, but it is still Flourine because it has 9 protons. So starting with a neutral atom it is possible that a Flourine atom could lose 9 electrons.