Answer to Question #202938 in Astronomy | Astrophysics for Prachi

Question

 Calculate the half-width of a spectral line of wavelength of λ= 550 nm when the 

temperature of the gas is 6 × 10⁵ K. Assume H atoms to be emitters.

Answer 1

According to http://hyperphysics.phy-astr.gsu.edu, for the Gaussian form of line

$\dfrac{\Delta\lambda}{\lambda_0} = 2\sqrt{2\ln2\cdot\dfrac{kT}{c^2}} = 2\sqrt{2\ln2\cdot\dfrac{1.38\cdot10^{-23}\cdot6\cdot10^5}{(3\cdot10^8)^2}} = 5.5\cdot10^{-4}.$

Therefore, $\Delta\lambda = 5.5\cdot10^{-4}\cdot5500\text{\AA} = 3\text{\AA} .$