The sun emits a light with maximum wavelength 510 nm, while another star X emits a light with maximum wavelength of 350nm. What is the ratio surface temperature of the sun and the star X?
Wavelength is the distance between two consecutive crests or troughs of a wave. It is a fundamental property of waves, including light and sound, determining their energy and frequency. Wavelength is inversely proportional to frequency and is commonly measured in meters, nanometers or micrometers, depending on the wave’s type and application.
Class 11 Physics Chapter 10 Thermal Properties of Matter focuses on understanding heat transfer mechanisms and temperature-related phenomena. It covers conduction convection and radiation, specific heat capacity, calorimetry, thermal expansion of solids liquids and gases and Newton’s law of cooling. This chapter explores practical applications of thermal properties and provides insights into real-life thermal processes for CBSE Exam 2024-25.
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To calculate the ratio of the surface temperatures of the Sun and star X, we use Wien’s displacement law:
λ_max × T = b
where:
– λ_max is the wavelength at maximum radiation,
– T is the temperature of the object,
– b is Wien’s constant (2.9 × 10⁶ nm·K).
The ratio of the temperatures is given by:
(T_sun / T_star_X) = λ_max_star_X / λ_max_sun
Substitute the given values:
– λ_max_sun = 510 nm,
– λ_max_star_X = 350 nm.
(T_sun / T_star_X) = 350 / 510 = 0.686
Thus, the ratio of surface temperatures is approximately 0.68.
The correct answer is 0.68.
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