UNIVERSITY OF SOUTH AFRICA
College of Science, Engineering and Technology
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
PHY3702
Assignment:1
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
PHY3702
Module:
Quantum Physics
Module Name
1
Assignment:
2026
Due Date:
Submitted in partial fulfilment of the requirements — UNISA
,UNISA | PHY3702 Assignment: 1
Question 1: Blackbody Radiation — Stefan-Boltzmann and Wien’s Laws
Question
Assuming that a given star radiates like a blackbody, estimate:
(a) the temperature at its surface,
(b) the wavelength of its strongest radiation,
when it emits a total intensity of I = 575 MW m−2 .
Solution
Given:
I = 575 MW m−2 = 575 × 106 W m−2
The Stefan-Boltzmann constant:
σ = 5.67 × 10−8 W m−2 K−4
The Stefan-Boltzmann law states:
I = σT 4
(a) Temperature at the Surface
Rearranging for T 4 :
I
T4 =
σ
Substituting values:
575 × 106
T4 =
5.67 × 10−8
T 4 = 1.0141 × 1016 K4
Taking the fourth root:
1/4
T = 1.0141 × 1016
Page 2 of 28
, UNISA | PHY3702 Assignment: 1
T ≈ 1.00 × 104 K
(b) Wavelength of Strongest Radiation
Wien’s displacement law states:
λmax T = 2.898 × 10−3 m K
Therefore:
2.898 × 10−3
λmax =
T
Substituting T = 1.00 × 104 K:
2.898 × 10−3
λmax =
1.00 × 104
λmax = 2.898 × 10−7 m
λmax ≈ 289 nm
This wavelength falls in the ultraviolet region of the electromagnetic spectrum.
Implementation Insight
Physical Meaning: A surface temperature of approximately 10,000 K is characteristic
of a hot blue-white star such as Vega or Sirius A. The peak wavelength of 289 nm
confirms emission primarily in the ultraviolet, consistent with stars of spectral class A.
Page 3 of 28
College of Science, Engineering and Technology
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
PHY3702
Assignment:1
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
PHY3702
Module:
Quantum Physics
Module Name
1
Assignment:
2026
Due Date:
Submitted in partial fulfilment of the requirements — UNISA
,UNISA | PHY3702 Assignment: 1
Question 1: Blackbody Radiation — Stefan-Boltzmann and Wien’s Laws
Question
Assuming that a given star radiates like a blackbody, estimate:
(a) the temperature at its surface,
(b) the wavelength of its strongest radiation,
when it emits a total intensity of I = 575 MW m−2 .
Solution
Given:
I = 575 MW m−2 = 575 × 106 W m−2
The Stefan-Boltzmann constant:
σ = 5.67 × 10−8 W m−2 K−4
The Stefan-Boltzmann law states:
I = σT 4
(a) Temperature at the Surface
Rearranging for T 4 :
I
T4 =
σ
Substituting values:
575 × 106
T4 =
5.67 × 10−8
T 4 = 1.0141 × 1016 K4
Taking the fourth root:
1/4
T = 1.0141 × 1016
Page 2 of 28
, UNISA | PHY3702 Assignment: 1
T ≈ 1.00 × 104 K
(b) Wavelength of Strongest Radiation
Wien’s displacement law states:
λmax T = 2.898 × 10−3 m K
Therefore:
2.898 × 10−3
λmax =
T
Substituting T = 1.00 × 104 K:
2.898 × 10−3
λmax =
1.00 × 104
λmax = 2.898 × 10−7 m
λmax ≈ 289 nm
This wavelength falls in the ultraviolet region of the electromagnetic spectrum.
Implementation Insight
Physical Meaning: A surface temperature of approximately 10,000 K is characteristic
of a hot blue-white star such as Vega or Sirius A. The peak wavelength of 289 nm
confirms emission primarily in the ultraviolet, consistent with stars of spectral class A.
Page 3 of 28
