According to Wien’s Displacement Law, how does the temperature of an object influence the wavelength of its peak emission?
Show answer & explanation
Correct answer: A
Explanation
Solution: The correct answer is The hotter the object, the shorter the wavelength at which it emits the most energy.
Explanation:
☛ Wien’s Displacement Law states that the wavelength at which a blackbody emits its maximum radiation (peak wavelength, λmax) is inversely proportional to its absolute temperature (T).
☛ Mathematically, it is expressed as λmax × T = b, where b is Wien’s displacement constant (approximately 2.898 × 10-3 m·K).
☛ As the temperature of an object increases, its peak emission shifts toward shorter wavelengths (higher frequencies and higher photon energies).
☛ Consequently, hotter objects emit peak radiation towards the blue or ultraviolet spectrum, while cooler objects emit peak radiation at longer wavelengths, such as red or infrared.
Extra Exam-Relevant Facts:
☛ Wilhelm Wien: Formulated this radiation law in 1893 and was awarded the Nobel Prize in Physics in 1911 for his discoveries regarding radiation laws.
☛ Astrophysical Application: Wien's law is used by astronomers to estimate the surface temperatures of stars based on their colour and peak emission wavelength.
☛ Stefan-Boltzmann Law: States that the total energy radiated per unit surface area of a blackbody is directly proportional to the fourth power of its absolute temperature (E ∝ T4).
☛ Planck’s Quantum Hypothesis: Max Planck mathematically derived Wien’s displacement law from his quantum radiation formula, effectively explaining blackbody radiation curves.
Important One-Liners for Upcoming Exams:
☛ What is the approximate value of Wien’s displacement constant (b)? → 2.898 × 10-3 m·K
☛ In which year was Wilhelm Wien awarded the Nobel Prize in Physics? → 1911
☛ According to radiation laws, which star has a higher surface temperature: blue or red? → Blue star
☛ Total radiant energy of a blackbody is proportional to which power of temperature according to Stefan-Boltzmann law? → Fourth power (T4)
☛ Who solved the blackbody ultraviolet catastrophe using the quantum hypothesis? → Max Planck (in 1900)