To measure the surface temperature of Venus, Mariner 2 measured emissions with wavelengths of 1.35 cm and 1.9 cm. The temperature of Venus is 730 K. What is the peak wavelength in the emission spectrum of Venus?
A)1.35 cm
B)1.9 cm
C)4
? m
D)6 nm

Question

To measure the surface temperature of Venus, Mariner 2 measured emissions with wavelengths of 1.35 cm and 1.9 cm. The temperature of Venus is 730 K. What is the peak wavelength in the emission spectrum of Venus?
A)1.35 cm
B)1.9 cm
C)4 
? m
D)6 nm

Quizplus · Accepted Answer

We can solve this problem using Wien's displacement law, which states that the peak wavelength λmax of the emitted radiation from a black body is inversely proportional to its temperature T:

λmax = b/T

where b is a constant (the Wien displacement constant), equal to 2.898 × 10^-3 m·K.

First, we need to convert the temperature of Venus from kelvin to Celsius:

T = 730 K = 457°C

Then, we can calculate the peak wavelength:

λmax = 2.898 × 10^-3 m·K / 457°C = 6.34 × 10^-6 m = 6.34 μm

Therefore, the answer is C: 4 μm.

To Measure the Surface Temperature of Venus, Mariner 2 Measured