Deck 37: The Foundations of Modern Physics

Question 1

A perfectly black sphere 18.0 cm in diameter is held at a temperature of 215°C.
(σ = 5.670 × 10^-8 W/m² ∙ K⁴,Wien displacement law constant is 2.90 × 10^-3 m ∙ K,
h = 6.626 × 10^-34 J ∙ s,c = 3.00 × 10⁸ m/s)
(a)Near what wavelength does this sphere radiate most strongly?
(b)If all the radiated energy were at the wavelength found in part (a),how many photons would the sphere emit each second?

Answer 1

(a)5.94 µm (b)9.79 × 10²¹ photons

Question 2

In the vicinity of what frequency does an object with a temperature of 1000 K radiate the largest amount of power? (c = 3.00 × 10⁸ m/s,Wien displacement law constant equals 2.90 × 10^-3 m ∙ K,σ = 5.670 × 10^-8 W/m² ∙ K⁴)

A)1.0 × 10¹⁴ Hz
B)8.0 × 10¹⁴ Hz
C)2.3 × 10¹⁴ Hz
D)6.7 × 10¹⁴ Hz
E)4.1 × 10¹⁴ Hz

Answer 2

1.0 × 10¹⁴ Hz

Question 3

An electric current through a tungsten filament maintains its temperature at 2800 K.Assume the tungsten filament behaves as an ideal radiator at that temperature.Near what wavelength does the filament emit the greatest power? (σ = 5.67 × 10^-8 W/m² ∙ K⁴,Wien displacement law constant is 2.9 × 10^-3 m ∙ K)

A)1000 nm
B)1200 nm
C)1400 nm
D)1600 nm
E)1800 nm

Answer 3

1000 nm

Question 4

An electric current through a tungsten filament maintains its temperature at 2800 K.Assume the tungsten filament behaves as an ideal radiator at that temperature.If the radiating area of the filament is 2.0 × 10^-6 m²,at what rate does it radiate energy? (σ = 5.670 × 10^-8 W/m² ∙ K⁴,Wien displacement law constant is 2.90 × 10^-3 m ∙ K)

A)5.5 W
B)7.0 W
C)8.5 W
D)10 W
E)11.5 W

Question 5

A perfectly black body at 100°C emits light of intensity I that has the strongest intensity near wavelength λ.The temperature of this body is now increased to 200°C.
(a)In terms of I,what is the intensity at which this hotter body radiates?
(b)In terms of λ,near what wavelength does light radiated from this hotter body have the strongest intensity?

Question 6

At absolute temperature T,a black body radiates its peak intensity at wavelength λ.At absolute temperature 2T,what would be the wavelength of the peak intensity?

A)16λ
B)2λ
C)λ
D)λ/2
E)λ/16

Question 7

What is the wavelength of peak emission for a black body at 37°C? (c = 3.0 × 10⁸ m/s,Wien displacement law constant is 2.9 × 10^-3 m ∙ K,σ = 5.67 × 10^-8 W/m² ∙ K⁴)

A)94 µm
B)9.4 µm
C)29 µm
D)7.8 µm
E)78 µm