Nuclear Key
1. Radon-222 undergoes alpha emission with a half-life of 3.823 days.
a. Write the balanced alpha emission reaction.
2α
222
4
86 Rn
+
218
84
Po
b. If 50.0 grams of radon gas were in a closed basement, how much would be left after 19.00 hours?
3.823 d = 0.693 / k so k = 0.18127 d-1
ln ( At / 50.0) = - 0.18127 d-1 (19.00 h)( 1 d / 24 h)
ln At - ln 50.0 = -0.1435
At = 43.3 grams
2. True or False regarding atom stability?
a. In general, calcium and smaller atoms are likely to be stable if their number of protons and neutrons
are equal. __ True _
b. Above uranium all isotopes are unstable AND below uranium all atoms have at least one stable
isotope. __ False
c. In general, an even number of protons and even number of neutrons is far more likely to be stable
than an odd number of protons and odd number of neutrons. __ True
3. Balance the following transmutation reactions:
a.
53
b.
238
c.
d.
24 Cr
+
4
2α
4
92U
14
7Ν
27
13Al
+
4
2α
0
2
1n
Whoops – neutron is 10n so can’t grade this one
α + __23490 Th_ + 2
__178 O___ +
+ ___42 α___
30
15P
+
1
0
0γ
1H
1
0n
4. What is the decay constant (k) for the radioactive isotope carbon-14 which has a half life of 5730 years?
How old is a bone that has only 77.2% of its carbon-14 remaining?
5730 y = 0.693 / k so k = 0.000121 y-1
ln ( 77.2 / 100.0) = - 0.000121 y-1 (t)
t = 2140 years old