SME
Remote Sensing · Problem type
Frequency and photon energy of a band
Use this for “A sensor band is centred at 850 nm in the near infrared. What are its frequency and the energy of one photon?”
Diagram
λ
=
c/f
=
3 ×
10
8
/(3.53
×
10
14
)
λ = 850 nm
E = hf
E
=
6.626 ×
10
-34
×
3.53 ×
10
14
E
=
2.34 ×
10
-19
J
In
electronvolts:
2.34 ×
10
-19
/(1.602
×
10
-19
)
=
1.46
eV
Higher frequency, shorter wavelength, more energy per photon: blue photons carry more than red.
This is an example. Type your own values to start a new problem.
f
Hz
=
3.00
×
10
8
÷
(
λ
×
10
−9
)
Solving the picture’s λ = c ÷ f for f gives f = c ÷ λ, with λ in metres.
E
Photon energy
calculated · eV
Formulas
f
=
3.00 ×
10
8
λ
×
10
-9
3.5294 ×
10
14
=
3.00 ×
10
8
850 ×
10
-9
E
=
6.626 ×
10
-34
×
f
1.602 ×
10
-19
1.4598
=
6.626 ×
10
-34
×
3.5294 ×
10
14
1.602 ×
10
-19
Assumptions
•
Light travels at c = 3.00 × 10⁸ m/s, and 1 nm is 10⁻⁹ m.
•
A photon carries E = hf, with Planck’s constant h = 6.626 × 10⁻³⁴ J·s; 1 eV is 1.602 × 10⁻¹⁹ J.
•
Together these give the shortcut E ≈ 1,240 ÷ λ, with λ in nm and E in eV.
Step-by-step
WE KNOW
λ = 850 nm
FIND
frequency (f), photon energy (E)
Step 1 · Find frequency (f)
Use f = 3.00 × 10⁸ ÷ (λ × 10⁻⁹)
The speed of light over the wavelength in metres is the number of waves passing each second.
f
=
3.00 ×
10
8
850 ×
10
-9
f
=
3.5294 ×
10
14
Hz
Step 2 · Find photon energy (E)
Use E = 6.626 × 10⁻³⁴ × f ÷ (1.602 × 10⁻¹⁹)
Planck’s constant times the frequency is the photon’s energy in joules; dividing by the joules in one electronvolt gives eV.
E
=
6.626 ×
10
-34
×
3.5294 ×
10
14
1.602 ×
10
-19
E
=
2.3386 ×
10
-19
1.602 ×
10
-19
E
=
1.4598
eV
Check
Put the numbers back in. Both sides should match.
3.5294 ×
10
14
=
3.00 ×
10
8
850 ×
10
-9
✓
1.4598
=
6.626 ×
10
-34
×
3.5294 ×
10
14
1.602 ×
10
-19
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
Electromagnetic radiation and sensors
Main lesson
Orbital period of a satellite
Use this for “An imaging satellite circles 705 km above the ground. How long does one orbit take, and how many orbits does it make in a day?”
The four resolutions
Use this for “A sensor records 12 bits a pixel and revisits every 16 days. Which kind of resolution is each?”