# Homework Help: Activity of substance after a certain time

1. Oct 26, 2014

### desmond iking

1. The problem statement, all variables and given/known data
A sample consists of 2g of a radioactive element. The molar mass of the element is 67g. If the half life of the element is 78 hours, the activity of the sample after 48 hours is ?

2. Relevant equations

3. The attempt at a solution
d(N)/dt = -λN
(2/67 x 6.02x10^23) (ln 2 )/ (78x 3600) = 4.4x10^16s^-1
A= acitivity
A = A_0 (0.5)^x
= (4.4x10^16) x (0.5)^(48/72)

= 2.7x10^16s^-1

but the ans given is 4.4x10^16s^-1

2. Oct 26, 2014

### haruspex

78, not 72.

3. Oct 26, 2014

### desmond iking

After changing 72 to 78.. Is my ans correct?

4. Oct 26, 2014

### haruspex

You posted that the answer given is 4.4x10^16s^-1, but that, as you showed, is the initial activity.
With the 72 changed to 78 your working looks right to me.

5. Oct 26, 2014

### desmond iking

So the ans given is correct? Or my working is correct?

6. Oct 26, 2014

### haruspex

The answer given is clearly wrong because it is the initial activity. It must be less after 48 hours.

7. Oct 27, 2014

### desmond iking

the ans should be
A = A_0 (0.5)^x
= (4.4x10^16) x (0.5)^(48/78)
= 2.87x10^16 ???

8. Oct 27, 2014

Looks right.