What is the total electric charge of 2.5 kg of (a) electrons and (b) protons?

What is the total electric charge of 2.5 kg of (a) electrons and (b) protons?

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  1. Answer:

    a

     [tex]Q_e  =  -4.39 *10^{11}  \  C [/tex]

    b

    [tex]Q_p  =  + 2.395*10^{-8} \  C [/tex]

    Explanation:

    Generally the number of electron in the given mass is  mathematically evaluated as

            [tex]N_e =  \frac{2.5}{m_e }[/tex]

    Here  m_e is the mass of electron with value [tex]m_e =  9.11 * 10^{-31} \  kg[/tex]

        =>  [tex]N_e =  \frac{2.5}{ 9.11 * 10^{-31} }[/tex]

           =>  [tex]N_e =2.74 *10^{30} \  electrons [/tex]

    The total electric charge is mathematically represented as

           [tex]Q_e  =  N_e  *  e[/tex]

    Here e is the charge on a single electron with value  [tex]e  =  1.60 *10^{-19}  \  C[/tex]

     So

              [tex]Q_e  =  -2.74 *10^{30}   *  1.60 *10^{-19} [/tex]

              [tex]Q_e  =  -4.39 *10^{11}  \  C [/tex]

    The  negative sign is because we are considering electron

    Generally the number of  protons in the given mass is  mathematically evaluated as

        [tex]N_p =  \frac{2.5}{m_p }[/tex]

    Here  m_p is the mass of electron with value [tex]m_e =  1.67 * 10^{-27} \  kg[/tex]

        =>  [tex]N_p =  \frac{2.5}{ 1.67 * 10^{-27} }[/tex]

           =>  [tex]N_p =1.497 *10^{27} \  protons [/tex]

    The total electric charge is mathematically represented as

           [tex]Q_p  = + N_p  *  e[/tex]

    Here p is the charge on a single proton with value  [tex]p  =  1.60 *10^{-19}  \  C[/tex]

     So

              [tex]Q_p  =  +1.497 *10^{27}   *  1.60 *10^{-19} [/tex]

              [tex]Q_p  =  + 2.395*10^{-8} \  C [/tex]

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