Answer:
The value is [tex]m = 6.48*10^{-5} \ g [/tex]
Explanation:
From the question we are told that
The total nuclear charge is [tex]Q_t = 3.0 \ C[/tex]
The atomic number is [tex]n = 13[/tex]
The number of neutrons is [tex]n = 14[/tex]
Generally the number of protons is mathematically represented as
[tex]N_p = \frac{Q_t}{p}[/tex]
Here p is the charge on a proton with the value [tex]p = 1.60 *10^{-19} \ C[/tex]
=> [tex]N_p = \frac{3}{p}[/tex]
=> [tex]N_p = \frac{3}{1.60 *10^{-19} }[/tex]
=> [tex]N_p = 1.875*10^19 \ protons [/tex]
Generally the number of atoms present is mathematically represented as
[tex]N_a = \frac{N_p}{n }[/tex]
=> [tex]N_a = \frac{ 1.875*10^19}{13}[/tex]
=> [tex]N_a = 1.44*10^{18} \ atoms [/tex]
Generally the number of moles of atom present is mathematically represented as
[tex]N = \frac{N_a}{A_n }[/tex]
Here [tex]A_n[/tex] is the Avogadro's number with a constant value
[tex]A_n = 6.023*10^{23}[/tex]
So
[tex]N = \frac{1.44*10^{18}}{6.023*10^{23} }[/tex]
=> [tex]N = 2.4*10^{-6} \ mol[/tex]
Generally the total mass is mathematically represented as
[tex]m = N * M[/tex]
Here M is the molar mass of aluminum with
[tex]M = 27 \ g/mol[/tex]
So
[tex]m = 2.4*10^{-6} * 27[/tex]
[tex]m = 2.4*10^{-6} * 27[/tex]
[tex]m = 6.48*10^{-5} \ g [/tex]
The mass of aluminum has a total nuclear charge of 3.0 C is 6.45 * 10⁻⁵ g
nuclear charge = 3.0 C
mass of proton = 1.60 * 10⁻¹⁹ C
Number of protons = 3.0/1.60 * 10⁻¹⁹ C
Number of protons = 1.875 * 10¹⁹ protons
atomic number = 13
Number of atoms = 1.875 * 10¹⁹/13
Number of atoms = 1.44 * 10¹⁸ atoms
moles of atoms = 1.44 * 10¹⁸/ 6.02 * 10²³
moles of atoms = 2.39 * 10⁻⁶ moles
molar mass of Aluminum is 27 g
mass of aluminum = 2.39 * 10⁻⁶ * 27
mass of aluminum = 6.45 * 10⁻⁵ g
Therefore, the mass of aluminum has a total nuclear charge of 3.0 C is 6.45 * 10⁻⁵ g
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