Irodov – Problems in General Physics

6.94. Particles of mass m and energy E move from the left to the
potential barrier shown in Fig. 6.3. Find:
(a) the reflection coefficient R of the barrier for E > U 0 ;
(b) the effective penetration depth of the particles into the region
x > 0 for E < Uo, i.e. the distance from the barrier boundary to
the point at which the probability of finding a particle decreases
e-fold.

t

up

0

Fig. 6.3.

6.95. Employing Eq. (6.2e), find the probability D of an electron
with energy E tunnelling through a potential barrier of width 1
and height U 0 provided the barrier is shaped as shown:
(a) in Fig. 6.4;
(b) in Fig. 6.5.

U 0

• 1

Fig. 6.4. Fig. 6.5.^ Fig. 6.6.

6.96. Using Eq. (6.2e), find the probability D of a particle of

mass m and energy E tunnelling through the potential barrier

shown in Fig. 6.6, where U (x) = U 0 (1 — x 2112 ).

6.3. Properties of Atoms. Spectra

• Spectral labelling of terms: x(L)j, where x = 2S + 1 is the multipli-
  city, L, S, T are quantum numbers,

L = 0, 1, 2, 3, 4, 5, 6,...

(L): S, P, D, F, G, H, I, ...

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