Complete Question
What mass of aluminum has a total nuclear charge of 2.9 C?
Aluminum has atomic number 13. Suppose the aluminum is all of the isotope with 14 neutrons.
Answer:
The mass is [tex]T_m = 6.252 *10^{-5}\ g[/tex]
Explanation:
From the question we are told that
The total nuclear charge is [tex]q = 2.9 \ C[/tex]
The atomic number is [tex]u = 13[/tex]
The number of neutron is [tex]k = 14[/tex]
Generally the number of positive charge is mathematically represented as
[tex]N = \frac{q}{p}[/tex]
here p is the charge on a single proton with value [tex]p = 1.60*10^{-19} \ C[/tex]
So
[tex]N = \frac{2.9}{1.60*10^{-19}}[/tex]
=> [tex]N = 1.813*10^{19} \ protons[/tex]
Now since 1 atom contains 13 proton
The number of atoms present is
[tex]a = \frac{1.813*10^{19}}{13}[/tex]
[tex]a = 1.395 *10^{18} \ atoms[/tex]
Then the number of moles present is mathematically represented as
[tex]n = \frac{a}{N_k}[/tex]
Where N_k is the Boltzmann constant with value
[tex]N_k = 6.023*10^{23}[/tex]
So
[tex]n = \frac{1.395 *10^{18}}{ 6.023*10^{23}}[/tex]
[tex]n = 2.315 *10^{-6}\ moles[/tex]
Generally one mole of aluminum is equal to 27 g
So
The total mass of aluminum is
[tex]T_m = n * 27[/tex]
=> [tex]T_m = 2.315 *10^{-6} * 27[/tex]
=> [tex]T_m = 6.252 *10^{-5}\ g[/tex]
