Cliffs AP Chemistry, 3rd Edition

Samples: Free-Response Questions

1.^20881 Tlundergoes β-decay. The half-life is 3.1 min.

(a) Write the nuclear equation.

(b) How long will it take for 1.00 gram of^20881 Tlto be reduced to 0.20 gram by decay?

(c) Given 11.00 grams of pure^20881 Tlinitially, how many grams of pure^20881 Tlwill remain

after 23.0 min?

Answer

1. Given:^20881 Tl_ib-decay t 12 /= 31. min
   (a) Restatement: Nuclear equation.

(^20881) Tl" (^20882) Pb+- (^01) e
(b) Restatement: Time for 1.00 g to reduce to 0.20 g.
.
11. kt
020
n^100
A
A
(^0) ==n
6
6
@
@
0 693. =kt 12 /
.

..
k 31 min min
==0 693 022 -^1

.

.

.

ln.

min

t 020100 min

022

(^173)
==# - 1
(c) Given: 11 00. g of^20881 Tlinitially.
Restatement: How many grams remain after 23 min?
logx.
xkt
2 303
(^0) =
.

..
k 31 min min
==0 693 022 -^1

.

.

log. min min.

x

11 00

2 303

==^022 -^1 #^2322

log^11 xx 00 == 22. "^111022.

x 0 = 0.070 g

Nuclear Chemistry