Question

The rate of decay of an Iodine-123 isotope is proportional to the mass
of isotope present at that time. The initial mass of the isotope was
200 g. Determine the mass of Iodine present after 39 days if the half
life period of the lodine isotope is approximately 13 hours.​

Answer 1

Answer:

Half Life follows first Order kinetics

enter image source here

This graph shows what is going on during the decay

As you can see from the graph the half life is 8 days

Lets do the math and verify it with the graph

Recall

t

1

2

=

ln

2

k

8

=

ln

2

k

k

=

ln

2

8

With this you can solve most problems regarding the above data

ln

(

A

o

A

t

)

=

k

t

ln

(

A

o

A

t

)

=

ln

2

8

⋅

24

=

3

ln

2

=

ln

2

3

=

ln

8

(

A

o

A

t

)

=

8

Now

Greater the concentration of a sample greater the mass in in it

C

∝

M

So

(

A

o

A

t

)

=

(

m

o

m

t

)

=

8

we have

m

o

=

64

g

64

m

t

=

8

⇒

m

t

=

8

g

Verifying with the graph

m

24 hours

=

12.5

%

m

o

=

12.5

⋅

10

−

2

⋅

m

o

=

12.5

⋅

10

−

2

⋅

64

=

8

g

Answer 2

Answer:

N=200/(2)^72 gms

Step-by-step explanation: