Answer:
37.50g of ⁹¹Nb will remain after 2040 years.
Explanation:
The rate of decay of a radioactive isotope obeys the following formula:
<em>(1)</em>
Where N is moles of atoms in time t, N₀ is initial moles of atoms, K is decay constant and t is time.
300.0g of niobium are:
300.0g × (1mol / 91g) = <em>3.297 moles of ⁹¹Nb</em>
It is possible to obtain decay constant from half-life, thus:
680 years = ln 2 / K
K = 1.019x10⁻³ years⁻¹
Replacing these values in (1):
N / 3.297 moles of ⁹¹Nb = -0.125
N = 0.4121 moles of ⁹¹Nb after 2040 years. In mass:
0.4121 moles of ⁹¹Nb × (91g / mol) = 37.50g of ⁹¹Nb will remain after 2040 years.