Answer to Question #173620 in Astronomy | Astrophysics for ANJU JAYACHANDRAN

Question

4b) Calculate the half-width of a spectral line of wavelength  = 550 nm when the

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

Answer 1

The line shape is Gaussian; the full width at half maximum intensity in Å,

$$\Delta\lambda_{1/2}^D = (7.16\times10^{-7})\,\lambda(T/M)^{1/2}\quad (1)$$

where T is the temperature of the emitters in K, and M the atomic weight in atomic mass units (amu)

In our case, λ = 550 nm, T=6 × 10⁵ K, M=1 amu

Using (1) we got:

$\Delta\lambda_{1/2}^D = (7.16\times10^{-7})\,\times550×10^{-9}(\frac{6×10^5}{1})^{1/2}$

$=3\times10^{-10}$

$$\Delta\lambda_{1/2}^D = 3Å$$

Answer:

$3\times10^{-10}$