Question

A common radio wavelength observed coming from astronomical objects is 21 cm. What temperature is associated with this radiation?

Answer 1

Answer:

The temperature associated with this radiation is 0.014K.

Explanation:

If we assume that the astronomical object behaves as a black body, the relation between its wavelength and temperature is given by Wien's displacement law.

$\lambda_{max}=\frac{b}{T}$

where,

λmax is the wavelength at the peak of emission

b is Wien's displacement constant (2.89×10⁻³ m⋅K)

T is the absolute temperature

For a wavelength of 21 cm,

$T=\frac{b}{\lambda _{max} } = \frac{2.89 \times 10^{-3} m.K }{0.21m} =0.014K$