Answer:
a
[tex]N_e = 906 \ electrons[/tex]
b
[tex]M = 9.43 *10^{-25} \ kg[/tex]
Explanation:
From the question we are told that
The total number of particles is n = 1470 particles
The the total amount of charge on the particles is [tex]Q = - 5.456*10^{-17} \ C[/tex]
Generally this total number of particles can be mathematically represented as
[tex]n = N_p + N_e[/tex]
Where [tex]N_p \ and \ N_e[/tex] represent the number of proton and electron respectively
=> [tex]N_p = 1470 - N_e[/tex]
Also the total charge of these particles can be mathematically represented as
[tex]Q = (N_p - N_e ) e[/tex]
Here e is the charge on a single electron or proton with value
The negative sign is due to the fact the electrons are negative signed
[tex]e = 1.60 *10^{-19} \ C[/tex]
[tex]-5.456*10^{-17} = ( 1470 -2N_e )* 1.60 *10^{-19} [/tex]
[tex]N_e = 906[/tex]
Thus
[tex]N_p = 1470 - 906[/tex]
[tex]N_p = 564[/tex]
Generally the mass of the system is mathematically represented as
[tex]M = N_e * M_e + N_p * M_p[/tex]
Here [tex]M_e \ and \ M_p \ are \ mass \ of \ electron \ and \ proton \ with \ values \\ M_e = 9.1 *10^{-31} \ kg \ and \ M_p = 1.67 *10^{-27} \ kg \ respectively[/tex]
So
[tex]M = 906 * 9.1 *10^{-31} + 564 * 1.67 *10^{-27}[/tex]
[tex]M = 9.43 *10^{-25} \ kg[/tex]
