Chapter Twelve Review

Short Answer

	1.	Describe the range of colours that would be seen when heating a piece of steel to 3000K.

	2.	A blacksmith is working with iron to make a horseshoe. If the iron had to be at least 3000K before it could be bent, how would the blacksmith know the temperature of the iron simply by looking at it?

	3.	Why was the theory of quanta considered radical in explaining energy of vibrating molecules or atoms?

	4.	What is meant by the threshold frequency of the photoelectric effect?

	5.	A light is shining on a piece of metal. As the intensity of the light is strengthened (i.e., becomes brighter), what will happen to the photoelectrons?

	6.	As the frequency of light increases, describe the effect on the photoelectrons.

	7.	Why would different metals have different work functions?

	8.	Why would alkali metals tend to have smaller work functions than other heavier metals?

	9.	Why is it difficult to associate momentum with a photon of light?

	10.	Why does a wave-particle duality exist for light?

	11.	What is a matter wave?

	12.	Why is it necessary to place a specimen in a vacuum if it is to be viewed by an electron microscope?

	13.	A scanning electron microscope requires the specimen to be coated by a thin layer of a metal, usually gold or platinum. Why is this layer required?

	14.	What caused the deflection of the alpha particles when they approached the nucleus in Thompson’s gold foil experiment?

	15.	If an alpha particle is directed at two nuclei of different mass and charge, one light (i.e., lithium) and the other heavy (i.e., silver), which nuclei will the alpha particle get closer to and why?

	16.	What happens to an atom that absorbs more energy than its ionization energy?

	17.	What occurs when an excited electron in an atom returns to its ground state of energy?

	18.	What is meant by Heisenberg’s uncertainty principle?

Problem

	19.	Calculate the energy of light with wavelength 486 nm. Give your answer in joules and in electron volts.

	20.	Calculate the frequency and wavelength of a photon with 6.2 ´ 104 eV of energy.

	21.	Calculate the frequency required to eject electrons from gold with a work function of 5.47 eV.

	22.	Would 449-nm blue light eject electrons from silver metal with a work function of 4.74 eV?

	23.	With what speed would an electron be ejected from sodium that has a work function of 2.36 eV when it is illuminated by 442-nm light?

	24.	Calculate the wavelength of light equivalent to an electron moving at 3.98 ´ 105 m/s.

	25.	Calculate the energy, in electron volts, of an X ray of frequency 1.32 ´ 1018 Hz.

	26.	A 112-kg satellite is given an escape velocity of 1.11 ´ 104 m/s to leave Earth’s orbit. What wavelength will the satellite experience at this speed?

	27.	What must the speed of an electron be to have a wavelength equivalent to 430-nm blue light?

	28.	Calculate the closest distance that an a particle of mass 6.6 ´ 10–27 kg and energy 5.1 MeV can get to an atom of uranium .

	29.	An a particle of mass 6.6 ´ 10–27 kg came closest to an atom of lead  with a distance of 4.8 ´ 10–14 m. At what velocity will the a particle rebound directly away if the collision is totally elastic?

	30.	An electron with energy 13.2 eV collides with an element, and the electron emerges with energy 4.5 eV. What wavelength of light would also be emitted along with the electron?

	31.	A wavelength of 431 nm is detected from a line spectrum. What change in energy level does this line represent if it is related to the ground state. Give your answer in electron volts..

	32.	Two spectral lines of wavelength 192 nm and 532 nm are emitted from the first and second energy levels to the ground state. What wavelength of photon would be emitted from the second to the first energy level?

	33.	What wavelength of photon could excite an electron from the third to the fifth energy state of hydrogen?

	34.	An electron with energy 0.45 eV has a velocity of 3.98 ´ 105 m/s. What is the uncertainty of its position?

Chapter Twelve Review
Answer Section

SHORT ANSWER

	1.	ANS:	
As the temperature increases, the colour of the metal will gradually change from red to yellow to white.

OBJ:	12.1	LOC:	ME1.01

	2.	ANS:	
As the temperature of the iron increases, its colour changes. By knowing the colour that corresponds to the temperature required, the blacksmith would be able to tell the temperature.

OBJ:	12.1	LOC:	ME1.01

	3.	ANS:	
The idea was radical because energy had been previously considered a continuous variable, capable of infinite small steps in changes. Quanta energy levels did not allow energies to be present between these fixed amounts.

OBJ:	12.1	LOC:	ME1.04

	4.	ANS:	
The threshold frequency is the minimum frequency of light (photons) that will eject a photoelectron from a piece of metal.

OBJ:	12.1	LOC:	ME1.03

	5.	ANS:	
The intensity of light will increase the number of photoelectrons (the current), but will not increase the speed of the ejected electrons.

OBJ:	12.1	LOC:	ME1.03

	6.	ANS:	
At a certain frequency, called the threshold frequency, electrons will begin to be ejected from a metal. As the frequency continues to increase, the speed of the electrons will also increase.

OBJ:	12.1	LOC:	ME1.03

	7.	ANS:	
Different metals require different amounts of energy (work) to release the electrons.

OBJ:	12.1	LOC:	ME1.03

	8.	ANS:	
They may require smaller work functions in that they have lower electron affinities. They tend to “lose” their electrons more easily because of their placement in the periodic table.

OBJ:	12.1	LOC:	ME1.03

	9.	ANS:	
Momentum is usually associated with an object that has mass and velocity. It is difficult to give momentum to a photon, a quanta of massless energy.

OBJ:	12.1	LOC:	ME1.03

	10.	ANS:	
Light experiments demonstrate that in certain cases light operates as a wave, and in other cases it behaves like a particle.

OBJ:	12.2	LOC:	ME1.03

	11.	ANS:	
It is the wavelength associated with objects that have mass. The wavelengths are extremely small according to de Broglie’s equation.

OBJ:	12.2	LOC:	ME1.04

	12.	ANS:	
A vacuum is necessary to prevent air molecules from scattering the beam of electrons.

OBJ:	12.2	LOC:	ME3.02

	13.	ANS:	
The thin layer of metal is designed to prevent a buildup of negative charge due to the electrons. Therefore, the negative charge does not start to repel the incoming beam of electrons.

OBJ:	12.2	LOC:	ME3.02

	14.	ANS:	
Alpha particles have a positive charge. When these positive charges approach the positive charge of the nucleus, they are repelled according to Coulomb’s law.

OBJ:	12.3	LOC:	ME1.04

	15.	ANS:	
The alpha particle will approach the lighter nuclei (lithium) more closely. The nucleus has a smaller charge and, therefore, would require a closer distance to exert a repulsive force.

OBJ:	12.3	LOC:	ME1.04

	16.	ANS:	
If an atom absorbs more energy than its ionization energy, the electron is removed from the atom leaving a positively-charged ion.

OBJ:	12.4	LOC:	ME1.04

	17.	ANS:	
It must give off the accumulated energy. It releases this energy as a photon of light with a wavelength equal to the amount of energy.

OBJ:	12.4	LOC:	ME1.04

	18.	ANS:	
The uncertainty principle states that an electron’s position and velocity cannot be determined at the same time with any degree of accuracy.

OBJ:	12.6	LOC:	ME1.04

PROBLEM

	19.	ANS:	

E = ?

The energy of the light is 4.09 ´ 10–19 J or 2.56 eV.

OBJ:	12.1	LOC:	ME1.03

	20.	ANS:	
E = 6.2 ´ 104 eV

The frequency of the photon is 1.5 ´ 1019 Hz.

The wavelength of the photon is 2.0 ´ 10–11 m.

OBJ:	12.1	LOC:	ME1.03

	21.	ANS:	

EK will have to be zero or greater for the electron to be ejected.

The frequency of light required would be 1.32 ´ 1015 Hz.

OBJ:	12.1	LOC:	ME1.03

	22.	ANS:	

No, an electron would not be ejected because the kinetic energy is not a positive value.

OBJ:	12.1	LOC:	ME1.03

	23.	ANS:	

v = ?

The electron would be ejected from the sodium with a speed of 3.98 ´ 105 m/s.

OBJ:	12.1	LOC:	ME1.03

	24.	ANS:	
m = 9.11 ´ 10–31 kg

p = mv
p = (9.11 ´ 10–31 kg)(3.98 ´ 105 m/s)
p = 3.626 ´ 10–25 kg·m/s

The wavelength of a photon equivalent to the electron is 1.83 nm.

OBJ:	12.2	LOC:	ME1.03

	25.	ANS:	

The energy of the X ray is 5.47 MeV.

OBJ:	12.2	LOC:	ME1.03

	26.	ANS:	

The satellite will have a wavelength of 5.33 ´ 10–40 m.

OBJ:	12.2	LOC:	ME1.04

	27.	ANS:	

v = ?

The electron must have a speed of 1.69 ´ 103 m/s.

OBJ:	12.2	LOC:	ME1.04

	28.	ANS:	
E = 5.1 MeV = 8.16 ´ 10–13 J
q1 a charge = 2(1.6 ´ 10–19 J) = 3.2 ´ 10–19 C
q2 U charge = 92(1.6 ´ 10–19 J) = 1.47 ´ 10–17 C

The closest distance that the a particle can be at is 5.2 ´ 10–14m.

OBJ:	12.3	LOC:	ME1.04

	29.	ANS:	
a mass = 6.6 ´ 10–27 kg
q = 3.2 ´ 10–19 C

Pb mass is not required.
q = 82 (1.6 ´ 10–19) = 1.31 ´ 10–17 C

The alpha particle will move away at 1.5 ´ 107 m/s.

OBJ:	12.3	LOC:	ME1.04

	30.	ANS:	

The wavelength of light that would be emitted would be 140 nm.

OBJ:	12.4	LOC:	ME1.03

	31.	ANS:	

This wavelength represents an energy change of 2.88 eV.

OBJ:	12.4	LOC:	ME2.01

	32.	ANS:	
192 nm	532 nm	

The wavelength of photon emitted from the second to the first energy level is 300 nm.

OBJ:	12.4	LOC:	ME2.01

	33.	ANS:	

The photon would have a wavelength of 1280 nm.

OBJ:	12.5	LOC:	ME2.01

	34.	ANS:	

	

The position of the electron would have an uncertainty of 3.20 ´ 1020 m.

OBJ:	12.6	LOC:	ME1.04