Question

The radius of a white dwarf, in kilometers, can be approximated by the expression where the mass is in solar masses and the radius is in km. A spectral line from a white dwarf spectrum observed at a wavelength of 540.002545207479 nm is recognized to be a line with true wavelength 540 nm. What is the mass of the white dwarf that is being observed?

The mass of the white dwarf is:  

radius -(-8(mass)13.8) 105

Answer 1

Gravitational redshift from a white dwarf is given by:

$\frac{\Delta \lambda}{\lambda} \approx \frac{GM}{Rc^2}$

Let M' be the mass in solar masses. Then, M' = M/1.989 x 10³⁰

substitute R = [ - 8M' + 13.8] x 10⁵ x 10³ m

then,

(540.002545207479-540) 540 GM,(1.989×1030) 113.8-8.11,1 × 108C2 Δλ λ

13.8-S 0.31975 8MP

=> M' = 1.240177 solar masses = 2.4667 x 10³⁰ kg

this is the mass of the white dwarf.