# Half life Problems by K0x8Dfd

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```									Name                                                                                  Practice Worksheet
Independent Study on Nuclear Chemistry                                                Half-life Problems
Reference Table “O” for Physical Setting/CHEMISTRY summarizes the types of radioactive particles (emanations)
that can be released or absorbed by a nucleus during the transmutation of a nuclide and half-lives for selected
OBJECTIVES:
 Define half-life and give examples.
 Solve half-life problems

REGENTS’ Major Understanding:
 Spontaneous decay can involve the release of alpha
particles, beta particles, positrons and/or gamma
radiation from the nucleus of an unstable isotope.
These emissions differ in mass, charge, and ionizing
power, and penetrating power. (3.1p)
 Nuclear reactions can be represented by equations
that include symbols which represent atomic nuclei
(with the mass number and atomic number),
subatomic particles (with mass number and charge),
and/or emissions such as gamma radiation. (4.4c).
 Each radioactive isotope has a specific mode and rate
of decay (half-life). (4.4a)
The following equation CAN be used to determine the
amount of radioisotope remaining. However, there are
multiple methods for solving half-life problems
t
1
m  final   m  initial   ( )  T
2
m final  final mass
minitial  initial mass
t  total time elapsed
T  half-life (Table N)
t
1
Fraction remaining  ( ) T
2
SAMPLE QUESTION:
Most chromium atoms are stable, but chromium-51 is an
unstable isotope with a half-life of 28 days. What fraction of
a sample of Cr-51 will remain after 168 days?
168
1                    1
Solve:      Fraction remaining  ( ) 28 = 0.015625 =
2                    64

SAMPLE QUESTION:

How much was present originally in a sample of chromium-51 if 0.75 g remains after 168 days?
168
1
Solve:       0.75  minitial ( ) 28                   48 g  minitial
2
Problem Set #1: Solve the following half-life problems using a method of your choice
1) Fluorine-21 has a half-life of 5.0 seconds. If you start with 25 g of fluorine-21, how many grams would remain
after 60.0 s?
2) If 10.0 mg of cesium-137 disintegrates over a period of 90.69 years, how many mg of cesium-137 would remain?
3) A sample of gold-198 has a mass of 30.0-g. How many days are required for the gold-198 to decay to 7.5-g?
4) After 21.04 years, 25.0-g of cobalt-60 remains unchanged. How much cobalt-60 was in the original sample?

Problem Set #2: Solve the following half-life problems using a method of your choice
1) After 62.0 hours, 1.0 g remains unchanged from a sample of 42 K . How much 42 K was in the original sample?
2) If 80.0 mg of a radioactive element decays to 10.0 mg in 30.0 minutes, what is the elements half-life, in minutes?
3) In 6.20 hours, a 100.0 gram sample of Ag-112 decays to 25.0 g What is the half-life of Ag-112 in hours?
4) What is the mass of K-42 remaining in a 16.0-g sample of K-42 after 37.2 hours?
5) If 3.0 g of Sr-90 in a rock remained unchanged in 1999, approximately how many grams of Sr-90 were present in
the original sample in 1943?
6) A sample of I-131 decays to 1.0 g in 40.35 days. What was the mass of the original sample?
7) What is the total mass of Rn-222 remaining in an original 160.0-mg sample of Rn-222 after 19.1 days?
8) A radioactive element has a half-life of 2 days. What is the fraction remaining after 6 days?

Problem Set #3

1.   As the temperature of a sample of a radioactive element decreases, the half-life of the element
(A) decreases       (B) increases            (C) remains the same             (D) varies with pressure
2.   If one-eighth of the mass of the original sample of a radioisotope remains unchanged after 4800 years,
the isotope could be
(A) H-3             (B) K-42                 (C) Sr-90               (D) Ra-226
3.   Which radioactive sample would contain the greatest remaining mass of the radioactive isotope after 10
years?
(A) 2.0 grams of Au-198                      (C) 2.0 grams of K-42
(B) 2.0 grams of P-32                        (D) 2.0 grams of Co-60
4.   Which of the following 10-g samples of radioisotope will decay to the greatest extent in 28 days?
(A) P-32            (B) Fr-220               (C)     Kr-85           (D) I-131
5.   As the pressure of a sample of a radioactive element decreases, the half-life will
(A) decrease                (B) increase             (C) remain the same
6.   Which sample will decay least over a period of 30 days?
(A) 10 g of P-32 -198       (B) 10 g of I-131        (C) 10 g of Au (D) 10 g of Rn-222