Question

please show all formulas/work

5. The decay constant of a radioactive source is 0.300/minute. - How much time must elapse before the activity is reduced to… (a) 85%? (b) 25%? (c) 5%?

B) The half-life of a radioactive source is 14.0 minutes. - How much time must elapse before the activity is reduced by… (a) 70%? (b) 45%? (c) 20%?

C) Radon-222 has a physical half-life of 30.0 days. A 10.24 microgram piece of this source is placed in storage. (a) How much mass is in the form of Radon-222 after 56 days? (b) How much time must elapse before the mass of Radon-222 is reduced to 5%?

D) A radioactive source has an initial activity of 3.00 milliCuries. After 10.0 hours, the activity of the source is 1.50 milliCuries. (a) What is the half-life of the source? (b) What is the decay constant of the source?

E) A radioactive source has a decay constant of 0.139/second. - How many radioactive atoms are present when the source has an activity of… (a) 3.00 microCuries? (b) 50.0 milliCuries? (c) 1.00 Curie. (see back of page for the remaining assignment)

F) A radioactive source has a half-life of 14.0 minutes. Its activity is 5.00 microCuries at 10:00 AM. (a) What is the decay constant of the source? (b) How many parents are present at 10:00 AM? (c) What is the activity at 10:42 AM? (d) How many parents are present at 10:42AM? (e) How many disintegrations occur between 10:00 AM and 10:42 AM? (f) How many daughters are born during this time interval?

G) From a single source with a decay constant of 0.150/hour, different groups of parent atoms are removed at certain times. Find the initial activity for each group at 10:00 am based on their corresponding final activities listed below. (a) Group 1: 40.2 mCi at noon. (b) Group 2: 25.3 mCi at 1:30 p.m. (c) Group 3: 58.2 µCi at 3:00 p.m. (d) Group 4: 8.31 µCi at 6:30 p.m.

H) From a Tc-99m source there are two groups of parent atoms that are removed from the source at different times. The first group is removed at 11:00 am and has an activity of 25.0 mCi. The second group is taken at 12:30 pm and has an activity of 30.0 mCi. - What is the minimum total activity of the combined groups at 10:00 am? The decay constant of Tc-99m is 0.1155/hour.

Answer 1

5

A)

a)

A_o = initial activity

$\lambda$ = decay constant = 0.3 /min = 5 x 10^-3 /s^-1

t = time taken

Given that ::

A = 0.85 A_o

Using the formula

A = A_o e^-$\lambda$t

0.85 A_o = A_o e^-(0.005)t

t = 32.5 sec

b)

Given that ::

A = 0.25 A_o

Using the formula

A = A_o e^-$\lambda$t

0.25 A_o = A_o e^-(0.005)t

t = 277.3 sec

c)

Given that ::

A = 0.05 A_o

Using the formula

A = A_o e^-$\lambda$t

0.05 A_o = A_o e^-(0.005)t

t = 599.15 sec

B)

half life = 14 min = 14 x 60 = 840 sec

$\lambda$ = decay constant

$\lambda$ = 0.693 / halflife = 0.693 /840 = 8.25 x 10^-4 = 0.000824

a)

Given that ::

A = 0.70 A_o

Using the formula

A = A_o e^-$\lambda$t

0.70 A_o = A_o e^-(0.000824)t

t = 438.86 sec

b)

a)

Given that ::

A = 0.45 A_o

Using the formula

A = A_o e^-$\lambda$t

0.45 A_o = A_o e^-(0.000824)t

t = 969.06 sec

c)

Given that ::

A = 0.20 A_o

Using the formula

A = A_o e^-$\lambda$t

0.20 A_o = A_o e^-(0.000824)t

t = 1953.2 sec