20 Worksheet
speed of light in a vacuum c = 3.0 × 108 m s−1
Planck constant h = 6.63 × 10−34 J s
1 eV = 1.6 × 10−19 J
Intermediate level
1
The figure below shows an electron making a transition between two energy levels
and the bright spectral emission line observed.
a
Explain why electromagnetic radiation is emitted when an electron jumps from
energy level E1 to energy level E2.
b Derive an expression for the frequency f of the radiation emitted.
c State and explain the position of the spectral line when an electron makes a transition
between energy levels E1 and E3.
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2
An electron in an atom can occupy four energy levels. With the help of an energy level
diagram, determine the maximum number of spectral emission lines from this atom.
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3
Lithium atoms emit red light of wavelength 670 nm. Calculate the difference between
the
energy levels responsible for this red light. [3]
4
The diagram below shows a hot solid, at a temperature of 5000 K, emitting a
continuous
spectrum.
State the type of spectrum observed from:
a position X
b position Y
c position Z.
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Higher level
5
The diagram below shows the some of the energy levels for a helium atom.
a Explain the significance of the energy levels being negative.
b When a helium atom is not excited, the electrons have an energy of −3.00 eV. This is
known as the stable state of the electrons. Calculate the minimum energy, in joules,
required to free an electron at this energy level. Explain your answer.
c The helium atom absorbs a photon of energy 1.41 eV.
i State the transition made by an electron.
ii Calculate the wavelength of the radiation absorbed by the helium atom.
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6
The figure below
shows the energy level
diagram for an atom of
mercury.
a Explain what is meant by the ground state. [1]
b Calculate the shortest wavelength
emitted by the atom. Explain your
answer.
[4]
Extension
7
For the hydrogen atom, the energy level En in joules is given by the equation
En  
2.18 10 18
n2
where n is an integer, known as the principal quantum number.
a
Calculate the energy level of the ground state (n = 1) and the energy level of the first
excited state (n = 2).
b Determine the wavelength of radiation emitted when an electron makes a transition from
the first excited state to the ground state. In which region of the electromagnetic spectrum
would you find a spectral line with this wavelength?
c In which region of the electromagnetic spectrum would you find the spectral line
corresponding to an electron transition between energy levels with principal quantum
numbers of 6 and 7? Justify your answer.
Total:
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Score:
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20 Marking scheme: Worksheet
1
a
The electron loses energy.
This energy appears as a photon of electromagnetic radiation.
b Energy of photon = E1 − E2
Therefore:
E  E2
hf = E1 − E2 or f  1
h
c The change in energy E is greater.
Hence the frequency of the radiation is greater. (f E)
The spectral line will be the right side of the line shown on the spectrum diagram.
2
There are six spectral lines.
E  hf 
3
[1]
[1]
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Correct transitions shown on the energy level diagram.
hc
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
34
6.63 10  3.0 10 8
E 
670 10 9
[1]
E = 2.97 × 10−19 J ≈ 3.0 × 10−19 J
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a Continuous spectrum
b Emission spectrum
c Absorption spectrum
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5
a
[1]
External energy has to be supplied to excite or free an electron.
(Allow: The electrons are trapped in an energy well.)
b An energy level of 0 eV means the electron is free from the atom.
The minimum energy is equal to 3.00 eV.
Energy needed to free electron = 3.00 × 1.6 × 10−19
Energy needed to free electron = 4.80 × 10−19 J
c i The difference between the energy levels −3.00 eV and −1.59 eV is equal to 1.41 eV.
Hence, an electron jumps from −3.00 eV energy level to −1.59 eV energy level.
hc
ii E  hf 

hc 6.63 10 34  3.0 10 8


E
1.411.6 10 19
 = 8.82 × 10−7 m
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3
6
a This is the lowest energy level occupied by an electron in an atom.
[1]
b The shortest wavelength corresponds to the change in energy between the two most widely
separated energy levels.
Hence, E = 10.43 eV
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hc
[1]
E  hf 


hc 6.63 10 34  3.0 10 8

E
10.43 1.6 10 19
[1]
 = 1.19 × 10−7 m
7
a
E1 = 
[1]
2.18 10 18
= –2.18 × 10−18 J
12
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2.18 10 18
= –5.45 × 10−19 J
22
hc
b E2 − E1 = E =

E2 = 

[1]
[1]
hc 6.63  10 34  3.0  10 8

E
(21.8  5.45)  10 19
[1]
 = 1.22 × 10−7 m
c
This spectral line lies in the ultraviolet region of the spectrum.
1
1
E = 2.18 × 10−18 ( 2  2 ) = 5.190 × 10−20 J
6
7

hc 6.63 10 34  3.0 10 8

E
5.190 10  24
[1]
[1]
 = 3.83 × 10−6 m (3.8 m)
This spectral line lies in the infrared region of the electromagnetic spectrum.
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