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Use the formula λm T = 0.29 cmK to obtain the characteristic temperature range for λm=5×10-7m
- a)7500 K
- b)7000 K
- c)6000 K
- d)6500 K
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Use the formulaλmT = 0.29 cmK to obtain the characteristic temp...
To find the characteristic temperature using Wien's displacement law, we start with the formula λm T = 0.29 cmK. We need to convert the wavelength λm from meters to centimeters: λm = 5×10-7 m = 5×10-5 cm. Substitute this into the formula: T = 0.29 cmK / 5×10-5 cm, which gives T = 5800 K. Due to rounding and context of black body radiation, this temperature is closer to 6000 K. Thus, the characteristic temperature range is approximately 6000 K.
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Community Answer
Use the formulaλmT = 0.29 cmK to obtain the characteristic temp...
Understanding the Formula
The formula used here is λmT = 0.29 cm·K, where:
- λm represents the wavelength of peak emission,
- T is the temperature in Kelvin.
This relationship helps us find the characteristic temperature when the wavelength is known.
Given Data
- λm = 5 × 10^-7 m (which is equivalent to 500 nm, or 0.5 μm)
Calculating Temperature
To find the temperature (T), rearranging the formula gives:
T = 0.29 cm·K / λm
First, convert λm from meters to centimeters:
- 5 × 10^-7 m = 5 × 10^-5 cm
Now, substitute λm into the equation:
T = 0.29 cm·K / (5 × 10^-5 cm)
Performing the Calculation
- T = 0.29 / 5 × 10^-5
- T = 0.29 / 0.00005
- T = 5800 K
Comparing with Options
The calculated temperature (5800 K) is closest to option 'c' which is 6000 K.
Conclusion
The correct answer is option 'C' (6000 K) as it aligns closely with the derived temperature from the given wavelength, confirming its suitability in the context of blackbody radiation.
This method effectively demonstrates how to determine characteristic temperatures using peak wavelength values in thermal physics.
The formula used here is λmT = 0.29 cm·K, where:
- λm represents the wavelength of peak emission,
- T is the temperature in Kelvin.
This relationship helps us find the characteristic temperature when the wavelength is known.
Given Data
- λm = 5 × 10^-7 m (which is equivalent to 500 nm, or 0.5 μm)
Calculating Temperature
To find the temperature (T), rearranging the formula gives:
T = 0.29 cm·K / λm
First, convert λm from meters to centimeters:
- 5 × 10^-7 m = 5 × 10^-5 cm
Now, substitute λm into the equation:
T = 0.29 cm·K / (5 × 10^-5 cm)
Performing the Calculation
- T = 0.29 / 5 × 10^-5
- T = 0.29 / 0.00005
- T = 5800 K
Comparing with Options
The calculated temperature (5800 K) is closest to option 'c' which is 6000 K.
Conclusion
The correct answer is option 'C' (6000 K) as it aligns closely with the derived temperature from the given wavelength, confirming its suitability in the context of blackbody radiation.
This method effectively demonstrates how to determine characteristic temperatures using peak wavelength values in thermal physics.
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