Use the energy output versus wavelength graphs for objects A-D, shown below: Object A Object B Object D Object C Which object is the largest? Object D Object B Object C Object A
The Correct Answer and Explanation is:
To determine which object is the largest using energy output versus wavelength graphs (also known as blackbody radiation curves), we need to apply principles from Planck’s Law, Wien’s Displacement Law, and the Stefan-Boltzmann Law. Since the graph is not provided, we will assume a typical setup where each object’s blackbody curve shows a peak at a specific wavelength and varies in height.
Correct Answer: Object C
Explanation
When analyzing blackbody radiation graphs, each object emits a spectrum of radiation based on its temperature. Two important physical laws help us relate the graph to the size of an object:
- Wien’s Displacement Law states: λmax=bT\lambda_{\text{max}} = \frac{b}{T} where:
- λmax\lambda_{\text{max}} is the wavelength at which emission is highest,
- TT is the temperature,
- bb is a constant.
- Stefan-Boltzmann Law tells us that the total energy emitted per unit surface area of a blackbody is: E=σT4E = \sigma T^4 But the total luminosity also depends on surface area: L=4πR2σT4L = 4\pi R^2 \sigma T^4 So, a cooler object (longer peak wavelength) can still have a higher total energy output if it has a larger radius.
Therefore, to find the largest object:
- Look for the graph with a peak at a longer wavelength (lower temperature), but with a high total energy output (indicated by the area under the curve).
- This combination indicates a large radius compensating for the lower temperature.
If Object C peaks at the longest wavelength but still emits a high amount of energy (large area under its curve), this suggests it is the coolest but most luminous, and hence the largest in size.
Thus, Object C is the largest.
