What mass of aluminum has a total nuclear charge of 2.9 c?

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What mass of aluminum has a total nuclear charge of 2.9 c?

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Thu Giang 2 months 2021-07-30T02:50:35+00:00 1 Answers 2 views 0

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    2021-07-30T02:52:13+00:00

    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   T_m  = 6.252 *10^{-5}\  g

    Explanation:

    From the question we are told that

       The  total nuclear charge is  q =  2.9 \  C

       The  atomic number is  u  =  13

        The number of neutron is  k  =  14

    Generally the number of positive charge is mathematically represented as

          N  = \frac{q}{p}

    here p is the charge on a single proton with value  p =  1.60*10^{-19} \  C

    So      

         N = \frac{2.9}{1.60*10^{-19}}

    =>    N = 1.813*10^{19} \ protons

    Now since 1 atom contains 13 proton

    The  number of atoms present is

            a =  \frac{1.813*10^{19}}{13}

           a =  1.395 *10^{18} \  atoms

    Then the number of moles present is mathematically represented as

          n = \frac{a}{N_k}

    Where  N_k is the Boltzmann constant with value  

           N_k  =  6.023*10^{23}

    So

           n  =  \frac{1.395 *10^{18}}{ 6.023*10^{23}}

            n = 2.315 *10^{-6}\  moles

    Generally one mole of aluminum is equal to 27 g

    So

     The total  mass of aluminum  is

              T_m  = n *  27

    =>        T_m  = 2.315 *10^{-6}  *  27

    =>        T_m  = 6.252 *10^{-5}\  g

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