Expert: Philip Stahl - 3/31/2010

Question
Hi:

In hydrogen, the transition from level 2 to level1 has a rest wavelength of 121.6 nm. suppose

you see this line at a wavelength of 120.5 nm in star A, at 121.2 nm in star B, at 121.9 nm in

star C, and at 122.9 nm in star D. Which stars are moving away? Which stars are coming toward

us? Which star is moving faster relative to us? No calculation

How can I find out which one is negative or positive without calculating?

Answer
Hello,

The key here is to note the "rest wavelength" and the other values relative to it. Recall that in a RED shift (wavelength longer than the rest value) the object is moving *away*. Thus, all those values for which:

L >  L(rest)

are moving away (in other words, the ones for 121.9nm, and 122.9 mm).

The rate of displacement is given by the magnitude difference. So the larger the difference the *faster* the motion away. Thus, the line at 122.9 nm (star D) is for an object moving faster away than for one at 121.9 nm(star C).

It works just in reverse for the blue shift, so you now are looking for wavelengths *smaller* than the rest value such that:

L < L(rest)

Thus, 120.5 nm for "star A" qualifies , as does 121.2 nm for B. Again, the more rapidly displacing star is the one with the greater difference from rest value. So, without calculating you know that A must be moving toward you faster than B is, since it has the greater magnitude difference - seen just from inspection.