Page 301 - Theory and Problems of BEGINNING CHEMISTRY

290 NUCLEAR REACTIONS [CHAP. 19

Supplementary Problems

19.19. Without consulting any references, text, or tables, add the correct symbol corresponding to each pair of subscript
0
0
12
4
12
3
0
1
1
and superscript. (Example: ?is C) (a) ?, (b) ?, (c) ?, (d) ?, (e) ?, (f ) ?, and (g) ?.
6 6 + 0 1 0 2 − 1
4
1
0
1
0
0
4
1
3
Ans. (a) β (b) γ (c) por H (d) n (e) α or He ( f ) β or 0 e (g) H
+ 0 1 1 0 2 2 − − 1
19.20. What is the difference between β and + β?
Ans. β is a high-energy electron. + β is a positron—a particle with the same properties as the electron except for
the sign of its charge, which is positive.
19.21. (a) How many alpha particles are emitted in the radioactive decay series starting with 235 U and ending with 207 Pb?
82
92
(b) How many beta particles are emitted? (c) Can you tell the order of these emissions without consulting reference
data? (d) Can you tell how many gamma particles are emitted?
Ans. (a) The mass number changes by 28 units in this series, corresponding to seven alpha particles (7×4 = 28).
(b) The seven alpha particles emitted would have reduced the atomic number by 14 units if no beta particles
had been emitted; since the atomic number is reduced by only 10 units, four (14 − 10) beta particles are also
emitted. (c) It is impossible to tell from these data alone what the order of emissions is. (d) It is impossible
to tell the number of gamma particles emitted, since emission of a gamma particle does not change either
the mass number or the atomic number.
19.22. What is the difference between radioactive decay processes and other types of nuclear reactions?
Ans. Other types of reactions require a small particle to react with a nucleus to produce a nuclear reaction;
radioactive decay processes are spontaneous with only one nucleus as a reactant.
19.23. In a certain type of nuclear reaction, one neutron is a projectile (a reactant) and two neutrons are produced. Assume
that each process takes 1 s. If every product neutron causes another event, how many neutrons will be produced (and
not be used up again) (a)in4sand(b)in10s?
Ans. n −→ 2n −→ 4n −→ 8n −→ 16 n
1s 1s 1s 1s
4
10
(a)In4s,2 = 16 neutrons are produced. (b)In10s,2 = 1024 neutrons will be produced.
19.24. In a certain type of nuclear reaction, one neutron is a projectile (a reactant) and two neutrons are produced. Assume
that each process takes 1 s. Suppose that half of all the product neutrons cause another event each, and the other half
escape from the sample. How many neutrons will be produced in the third second?
Ans. Two.
One escapes One escapes
n 2 n 2 n 2 n
One reacts One reacts
The reaction continues with the same number of neutrons being produced as started the reaction in the first
place.

19.25. Can the half-life of an isotope be affected by changing the compound it is in?
Ans. No. The chemical environment has a negligible effect on the nuclear properties of the atom.

19.26. How many beta particles are emitted in the decomposition series from 238 Uto 206 Pb?
82
92
Ans. The number of alpha particles, calculated from the loss of mass number, is 8, because the mass number
was lowered by 32. The number of beta particles is equal to twice the number of alpha particles minus the
difference in atomic numbers of the two isotopes.
(2 × 8) − 10 = 6
Six beta particles are emitted. (See Example 19.7 and Problem 19.21.)