E
hxf
Energy here measured in Joules (J)
Frequency measured in Hertz (Hz)
h (Planck’s constant)
h = 6.626 x 10-34 Js
1electron volt = 1.6 x 10 -19 Joules
What energy would result from radiation with a frequency of 1Hz?
Must use frequency measured in Hertz (Hz) so use f = 1Hz Energy=Planck’s Constant x frequency (E=hxf)
Always use Planck’s Constant 6.626x10-34 Js (The answer will give energy in Joules (J))
Into calculator (choose which line as appropriate for your calculator):
6
6
.
.
6
6
2
2
6
6
exp
x10x
3
(-)
4
3
+/4
x
x
1
1
=
=
Answer: 6.626x10-34 J
3
What energy would result from radiation with a frequency of 1000Hz (sometimes written as 1x10 Hz)
Must use frequency measured in Hertz (Hz) so use f = 1x103Hz
Energy=Planck’s Constant x frequency (E=hxf)
Always use Planck’s Constant 6.626x10-34 Js (The answer will give energy in Joules (J))
Into calculator (choose which line as appropriate for your calculator):
6
6
.
.
6
6
2
2
6
6
exp
x10x
3
(-)
4
3
+/4
x
x
1
1
exp
x10x
3
3
=
=
Answer: 6.626x10-31 J
6
What energy would a typical radio wave photon have for absolute radio 1215kHz (1215000 Hz or 1.215 x 10 Hz)?
Must use frequency measured in Hertz (Hz) so use f = 1.215x106Hz
Energy=Planck’s Constant x frequency (E=hxf)
Planck’s Constant = 6.626x10-34 Js (The answer will give energy in Joules (J))
Into calculator (choose which line as appropriate for your calculator):
6
6
.
.
6
6
2
2
Answer: 8.05x10-28 J
6
6
exp 3
x10x (-)
4
3
+/4
x
x
1
1
.
.
2
2
1
1
5
5
exp 6
x10x 6
=
=
18
What photon energy would a typical X-ray have if using a frequency of 1.5x10 Hz?
Must use frequency measured in Hertz (Hz) so use f = 1.5x1018Hz
Energy=Planck’s Constant x frequency (E=hxf)
Planck’s Constant = 6.626x10-34 Js (The answer will give energy in Joules (J))
Into calculator (choose which line as appropriate for your calculator):
6
6
.
.
6
6
2
2
6
6
exp 3
x10x (-)
4
3
+/4
x
x
1
1
.
.
5
5
exp 1
x10x 1
8
8
=
=
Answer: 9.94x10-16 J
For each spectra:
1)
2)
3)
4)
What is the accelerating voltage?
What is the maximum energy in eV?
What is the maximum energy in Joules?
What is the max frequency of the x-rays produced?
1) Accelerating voltage =
2) Maximum energy in eV =
3) Maximum energy in Joules
Large spectra: 100kV
Large spectra: 100keV
Smaller spectra: 60kV
Smaller spectra: 60keV
100keV = 100,000 eV = 1 x 105eV
Large spectra, energy in eV = 100keV
To convert eV to Joules multiply the amount in eV by 1.6x10-19
Into calculator (choose which line as appropriate for your calculator):
1
1
exp
x10x
5
5
x
x
1
1
.
.
6
6
exp
x10x
1
(-)
9
1
+/9
=
=
+/9
=
=
Answer, Large spectra = 1.6 x 10-14 J
60keV = 60,000 eV = 6 x 104 eV
Smaller spectra, energy in eV = 60keV
To convert eV to Joules multiply the amount in eV by 1.6x10-19
Into calculator (choose which line as appropriate for your calculator):
6
6
exp
x10x
4
4
x
x
1
1
Answer, Smaller spectra = 9.6 x10-15J
.
.
6
6
exp
x10x
1
(-)
9
1
4) Using the triangle, Frequency = Energy / Planck’s constant F = E/h (Must use energy measured in Joules)
(Just to be clear - the ‘/’ line means ‘divided by’)
Larger spectra: energy = 1.6 x 10-14 J
Into calculator (choose which line as appropriate for your calculator):
1
1
.
.
6
6
exp 1
x10x (-)
4
1
+/4
/
/
6
6
.
.
6
6
2
2
6
6
exp 3
x10x (-)
4
3
+/4
=
=
6
6
exp 3
x10x (-)
4
3
+/4
=
=
Answer, Larger spectra = 2.4 x 1019Hz
Smaller spectra: Energy = 9.6 x10-15J
Into calculator (choose which line as appropriate for your calculator):
9
9
.
.
6
6
exp 1
x10x (-)
5
1
+/5
/
/
6
6
.
.
6
6
2
2
Answer, Smaller spectra = 1.4 x 1019Hz
Homework sheet
What energy, in Joules, would result from radiation with a frequency of 1.5Hz?
What would this be in electron volts?
Must use frequency measured in Hertz (Hz) so use f = 1.5Hz
Energy=Planck’s Constant x frequency (E=hxf)
Planck’s Constant = 6.626x10-34 Js (The answer will give energy in Joules (J))
Into calculator (choose which line as appropriate for your calculator):
6
6
.
.
6
6
2
2
6
6
exp
x10x
3
(-)
4
3
+/4
x
x
1
1
.
.
5
5
=
=
Answer: 9.9 x 10-34J
What energy, in Joules, would result from radiation with a frequency of 6000Hz (sometimes written
as 6x103Hz or 6kHz). What would this energy be in electron Volts?
Must use frequency measured in Hertz (Hz) so use f = 6x103Hz
Energy=Planck’s Constant x frequency (E=hxf)
Planck’s Constant = 6.626x10-34 Js (The answer will give energy in Joules (J))
6
6
.
.
6
6
2
2
Answer in Joules: 3.98 x 10-30J
6
6
exp
x10x
3
(-)
4
3
+/4
x
x
6
6
exp
x10x
3
3
=
=
To convert Joules to eV divide the amount in Joules by 1.6x10-19
Into calculator (choose which line as appropriate for your calculator):
3
3
.
.
9
9
8
8
exp
x10x
3
(-)
0
3
+/0
/
/
1
1
.
.
6
6
exp
x10x
1
(-)
9
1
+/9
=
=
Answer in eV: 2.5 x 10-11eV
What energy in Joules, would a typical radio wave photon have for Talksport radio 1053kHz
(1215000 Hz or 1.215 x 106 Hz)? What would this be in electron volts?
Must use frequency measured in Hertz (Hz) so use f = 1.215x106Hz
Energy=Planck’s Constant x frequency (E=hxf)
Planck’s Constant = 6.626x10-34 Js (The answer will give energy in Joules (J))
Into calculator (choose which line as appropriate for your calculator):
6
6
.
.
6
6
2
2
6
6
exp 3
x10x (-)
4
3
+/4
x
x
1
1
.
.
2
2
1
1
.
.
6
6
exp
x10x
5
5
exp 6
x10x 6
=
=
Answer: 8.05x10-28 J
To convert Joules to eV divide the amount in Joules by 1.6x10-19
Into calculator (choose which line as appropriate for your calculator):
8
8
.
.
0
0
5
5
exp
x10x
2
(-)
8
2
+/8
/
/
1
1
1
(-)
9
1
+/9
=
=
Answer in eV: 5.0 x 10-9eV
What photon energy, in joules would a typical X-ray have if using a frequency of 1.6x1018 Hz?
(1600000000000000000Hz)
Must use frequency measured in Hertz (Hz) so use f = 1.6x1018Hz
Energy=Planck’s Constant x frequency (E=hxf)
Planck’s Constant = 6.626x10-34 Js (The answer will give energy in Joules (J))
Into calculator (choose which line as appropriate for your calculator):
6
6
.
.
6
6
2
2
Answer: 1.06x10-15 J
6
6
exp 3
x10x (-)
4
3
+/4
x
x
1
1
.
.
6
6
exp 1
x10x 1
8
8
=
=
To convert Joules to eV divide the amount in Joules by 1.6x10-19
Into calculator (choose which line as appropriate for your calculator):
1
1
.
.
0
0
6
6
exp
x10x
1
(-)
5
1
+/5
Answer in eV: 6.6 x 103eV
/
/
1
1
.
.
6
6
exp
x10x
1
(-)
9
1
+/9
=
=
(6625 eV = 6.6keV)
For an x-ray tube operating at 50kV, what is the maximum possible energy in eV?
What is this maximum energy in joules?
What would the frequency of these x-rays be?
Accelerating voltage =
Maximum energy in eV =
Maximum energy in Joules
50kV
50keV
Energy in eV = 50keV
50keV = 50,000 eV = 5 x 104eV
To convert eV to Joules multiply the amount in eV by 1.6x10-19
Into calculator (choose which line as appropriate for your calculator):
5
5
exp
x10x
4
4
x
x
1
1
.
.
6
6
exp
x10x
1
(-)
9
1
+/9
=
=
Answer, 8 x 10-15J
Using the triangle, Frequency = Energy / Planck’s constant F = E/h (Must use energy measured in Joules)
Larger spectra: energy = 1.6 x 10-14 J
Into calculator (choose which line as appropriate for your calculator):
8
8
exp 1
x10x (-)
5
1
Answer, 1.2 x 1019Hz
+/5
/
/
6
6
.
.
6
6
2
2
6
6
exp 3
x10x (-)
4
3
+/4
=
=