Page 14 - 83 basic knowledge of astronomy

Z n to Z m (Figure 13). The frequency of the absorbed or emitted radiation
is determined by the equation:

hν mn = E n − E m , (8)

where h is the Planck constant (h = 6.626 × 10 −34 J s).

Z n E=E n

hνmn=En-Em hνmn=En-Em
Z m E=E m

Z 3 E=E 3
Z 2 E=E 2
Z 1 E=E 1

Figure 13: Energy levels and transitions with emission (left–hand arrow) or
absorption (right–hand arrow) of radiation.

The energy levels here may be distributed continuously (continuum emis-
sion) or discretely (line emission). Note that even in the discrete level case,
the frequency is spread over a finite ‘line width’, due to the Doppler shifts in
randomly moving gaseous media in the universe.
Three kinds of transitions may occur between these two states (Figure
14), as follows:

(1) Spontaneous emission Z n → Z m
The spontaneous emission emerges due to a transition which occurs ‘by
itself’, without any external influence (Figure 15). The probability df sp for
the spontaneous emission to occur within a small solid angle dΩ towards a
direction -s, within a small frequency bandwidth dν around the frequency
ν mn = (E n − E m ) / h, and during a small time interval dt, must be propor-
tional to dν dΩ dt. Therefore, the probability can be expressed through a

14