Calculating Initial Decay Rate of Ga-67 Isotope

[says]

Homework Statement

An initially pure 3.4 g sample of Ga-67, an isotope with a half life of 78 hr.
What is its initial decay rate?

Note: Molar Mass values given in tables for chemical elements are for natural mix isotopic ratios. (i.e. the relative percentages of each isotope normally present in natural samples). The Molar Mass (in g/mol) for a pure isotope is equal to its atomic mass (in amu). (Answer in Bq, correct to 3 significant figures)

Avogadro's Number = 6.022045*10²³ g/mol
Ga-67 = 66.9282049 u = 66.9282049 g/mol
Half-life = T_1/2 = 78 Hr

Homework Equations

N = [ Avogadro's Number / 66.9282049 g/mol ] * 3.4 g
λ = ln(2) / T_1/2
Decay Rate = -λ*N

The Attempt at a Solution

N = [ 6.022045*10²³ g/mol / 66.9282049 g/mol ] * 3.4 g
= 3.059241321 * 10²²

λ = ln(2) / 280800
= 0.00000246847

Decay Rate = 0.00000246847 * 3.059241321 * 10²²
= 7.5516454*10¹⁶ Bq
= 7.55*10¹⁶ Bq (Correct to 3 sig figs)

This doesn't seem correct. I've got the atomic mass and therefore the molar mass of Ga-67, but to calculate N (nuclei) should I have subtracted the electrons from the atomic mass / molar mass?

 

[mfb]

Ga-67 = 66.9282049 u = 66.9282049 g/mol

While this is right, you are supposed to take another value: "The Molar Mass (in g/mol) for a pure isotope is equal to its atomic mass (in amu)"
The difference is large enough to influence the final result with 3 significant figures.

The electrons are fine, they are still part of the sample so there is nothing to subtract.

 

[says]

What other value should I use for the molar mass of Ga-67? Is there a way of converting the atomic mass I have to the correct molar mass to use in this question?

 

[mfb]

A sorry I misread the quoted part, somehow I thought the problem statement suggested to use 67 u as mass (not so uncommon in problems to neglect the difference between A and mass in u).
If this is an online test without limited attempts, you can try that.

I get the same answer as you so I don't know where the problem is.

 

[says]

1 attempt only I'm afraid!

Decay Rate = -λ*N

so should it be = - 7.55*1016 Bq?

 

[mfb]

Yes.