If a star has a surface temperature of 21,000K, at what electromagnetic wavelength does the star emit its maximum amount of energy?

Question

BlackTom AI · Accepted Answer

To determine where a hot star emits its maximum energy, we apply Wien's displacement law, which links the peak wavelength lambda_max to the temperature T via lambda_max = b / T, where b ≈ 2.898 × 10^-3 m·K.

Option 1: 0.1 micrometers (0.1 μm = 1.0 × 10^-7 m). Using T = b / lambda_max, this gives T ≈ (2.898 × 10^-3) / (1.0 × 10^-7) ≈ 29,000 K. At a temperature of 21,000 K, 0.1 μm is in the right ballpark for a very blue, high-energy peak; the calculation is consistent with a peak near this small wavelength.

Option 2: 1.0 micrometers (1.0 μm = 1.0 × 10^-6 m). If lambda_max were 1.0 μm, then T ≈ (2.898 × 10^-3) / (1.0 × 10^-6) ≈ 2,898 K, which is far cooler than 21,000 K. This would place the peak in the infrared, not in the ultraviolet, so this is inconsistent with the given temperature.

Option 3: 0.5 micrometers (0.5 μm = 5.0 × 10^-7 m). Here, T ≈ (2.898 × 10^-3) / (5.0 × 10^-7) ≈ 5,796 K. This is still much cooler than 21,000 K, indicating a peak at a longer wavelength than the star’s actual maximum emission.

Option 4: 10 micrometers (10 μm = 1.0 × 10^-5 m). Then T ≈ (2.898 × 10^-3) / (1.0 × 10^-5) ≈ 290 K, which corresponds to a very cool object emitting in the far-infrared. This is far from the 21,000 K stated and clearly not the peak for such a hot star.

Synthesis: Since hotter objects peak at shorter wavelengths, the 21,000 K star should have its peak in the ultraviolet region, near a wavelength on the order of 0.1 μm. Among the options, 0.1 μm best matches the high temperature and Wien’s law relationship, while the other choices place the peak at infrared or misrepresent the temperature scale.

Additional note: Real stars emit across a range of wavelengths around the peak, but Wien’s law provides the most direct estimate for the peak emission wavelength given the temperature. The mismatch in the other options arises because they correspond to temperatures far from 21,000 K, hence the incorrect predictions for lambda_max.

If a star has a surface temperature of 21,000K, at what electromagnetic wavelength does the star emit its maximum amount of energy?单项选择题

类似问题

The earth is much cooler than the Sun, but it also emits radiation. The earth’s peak wavelength of emission is _______ compared to the Sun’s peak wavelength.

A black body glowing in blue color is at a higher temperature than another black body glowing in yellow color.

A human body with a typical temperature of 300K emits its maximum electromagnetic energy at 10 micrometers, which is in the infrared range and far from the visible wave spectrum. Why can we see each other?

Which term best represents the relation between a blackbody and radiant energy? A blackbody is an ideal _______ of radiant energy.

Stefan-Boltzmann Law states that the total amount of energy emited by a blackbody is proportional to the temperature of the blackbody in Kelvin ...

A human body has a typical temperature of 97F, or about 300K, therefore at what wavelength do we emit the maximum amount of electromagnetic radiation?

Stefan-Boltzmann Law states that the total amount of energy emited by a blackbody is proportional to the temperature of the blackbody in Kelvin ...

Given the sun has a surface temperature of approximately 6,000K, over what electromagnetic wave spectrum does the sun emit its maximum amount of energy?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单