Activity of substance after a certain time

[desmond iking]

Homework Statement

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 ?

Homework Equations

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)[/B]
= 2.7x10^16s^-1

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

 

[haruspex]

= (4.4x10^16) x (0.5)^(48/72)

78, not 72.

 

[desmond iking]

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

 

[haruspex]

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

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.

 

[desmond iking]

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

 

[haruspex]

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

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

 

[desmond iking]

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

 

[haruspex]

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

Looks right.