Worked Solutions
Chapter 3
Question 16
Complete the following nuclear equations:
(a) 238
4

U
--
+
He
2
92
Answer: When a
238
U isotope undergoes alpha decay, its atomic number decreases by 2,
while its mass number decreases by 4:
238
U
92

(b)
234
Th
90
4
He
2
+
3

H
--
0
e
-1
+
1
Answer: When a 3H isotope undergoes beta decay, its atomic number increases by 1, while
its mass number remains the same:
3
H
1
3

(c) 239

Pu
0
He
2
--
+
4
He
2
+
93
Answer: When a
239
e
-1
Pu isotope undergoes alpha decay, its atomic number decreases by 2,
while its mass number decreases by 4:
239
235

Pa
91
Pu
93
(d)
4
He
+
2
32
0
P

--
+
15
e
-1
Answer: When a 32P isotope undergoes beta decay, its atomic number increases by 1, while
its mass number remains the same:
32
32
P
15

0
S
16
+
e
-1
1
(e) 212
Po
84

Answer: When a
212
--
4
He
2
+
Po isotope undergoes alpha decay, its atomic number decreases by 2,
while its mass number decreases by 4:
212
Po
84

(f)
208
Pb
82
24
4
+
0

Na
He
2
--
+
e
11
-1
Answer: When a 24Na isotope undergoes beta decay, its atomic number increases by 1, while
its mass number remains the same:
24
24
Mg
12

Na
11
(g) 226
0
+
e
-1
4

Ra
--
+
88
He
2
Answer: When a
226
Ra isotope undergoes alpha decay, its atomic number decreases by 2,
while its mass number decreases by 4:
226
Ra
88
(h)
222

4
Rn
+
He
86
2
131
0

I
--
53
+
e
-1
Answer: When an 131I isotope undergoes beta decay, its atomic number increases by 1, while
its mass number remains the same:
131
131
I
53

0
Xe
54
+
e
-1
2
Question 19
The radioisotope cobalt-60 has a half-life of 5.26 years. How many years would it take 2g of
cobalt-60 to decay to 0.25g?
Answer:
Since the half-life of cobalt-60 is 5.26 years, the original 2g would have halved to 1g after
5.26 years, the 1g would have halved to 0.5g after a further 5.26 years, and the 0.5g would
have halved to 0.25g after a further 5.26 years. Thus it would take 15.78 years for 2g of
cobalt-60 to decay to 0.25g.
Question 31 (b)
Complete the following nuclear equations:
(i)
222
Rn
86

Answer: When a
222
--
4
He
2
+
Rn isotope undergoes alpha decay, its atomic number decreases by 2,
while its mass number decreases by 4:
222
218

Po
84
Rn
86
(ii)
13
B
5

+
4
He
2
--
0
+
e
-1
Answer: When a 13B isotope undergoes beta decay, its atomic number increases by 1, while
its mass number remains the same:
13
B
5
(iii)

196
Au
79
Answer: When a
13
C
6

196
0
e
+
-1
--
+
4
He
2
Au isotope undergoes alpha decay, its atomic number decreases by 2,
while its mass number decreases by 4:
3
196

Au
79
192
Ir
77
4
He
2
+
(iv)
42
0

K
--
+
e
19
-1
Answer: When a 42K isotope undergoes beta decay, its atomic number increases by 1, while
its mass number remains the same:
42

K
19
42
Ca
20
+
0
e
-1
(v)
185
W
74

185
Answer: When a
--
4
He
2
+
W isotope undergoes alpha decay, its atomic number decreases by 2,
while its mass number decreases by 4:
185
W
75

181
Hf
72
+
4
He
2
(vi)
45
Ca
20

0
--
+
e
-1
Answer: When a 45Ca isotope undergoes beta decay, its atomic number increases by 1, while
its mass number remains the same:
45
Ca
20

45
Sc
21
0
+
e
-1
(vii)
223
4
Ra
88

--
+
He
2
4
Answer: When a
223
Ra isotope undergoes alpha decay, its atomic number decreases by 2,
while its mass number decreases by 4:
223
219
Rn
86

Ra
88
4
He
2
+
(viii)
112
0

Ag
--
+
e
47
-1
Answer: When a 112Ag isotope undergoes beta decay, its atomic number increases by 1, while
its mass number remains the same:
112

Ag
112
Cd
47
+
48
0
e
-1
(ix)
239
U
92
239
 Np
93
+
--
Answer: The atomic number of 239U increases by 1, while its mass number remains the same.
This means that it has undergone beta decay:
239
U
92
239
Np
93

0
+
e
-1
(x)
232
Th
90
228

Ra
+
--
88
Answer: The atomic number of 232Th decreases by 2, while its mass number decreases by 4.
This means that it has undergone alpha decay:
232
Th
90

228
Ra
88
+
4
He
2
5