Respuesta :
Answer:
0.02442 × 10⁻⁹
Explanation:
Given:
Diameter of copper ball = 2.00 mm = 0.002 m
Charge on ball = 40 nC = 40 × 10⁻⁹ C
Density of copper = 8900 Kg/m³
Now,
The number of electrons removed, n = [tex]\frac{\textup{Charge on ball}}{\textup{Charge of an electron}}[/tex]
also, charge on electron = 1.6 × 10⁻¹⁹ C
Thus,
n = [tex]\frac{40\times10^{-9}}{1.6\times10^{-19}}[/tex]
or
n = 25 × 10¹⁰ Electrons
Now,
Mass of copper ball = volume × density
Or
Mass of copper ball = [tex]\frac{4}{3}\pi(\frac{d}{2})^3[/tex] × 8900
or
Mass of copper ball = [tex]\frac{4}{3}\pi(\frac{0.002}{2})^3[/tex] × 8900
or
Mass of copper ball = 0.03726 grams
Also,
molar mass of copper = 63.546 g/mol
Therefore,
Number of mol of copper in 0.03726 grams = [tex]\frac{ 0.03726}{63.546}[/tex]
or
Number of mol of copper in 0.03726 grams = 5.86 × 10⁻⁴ mol
and,
1 mol of a substance contains = 6.022 × 10²³ atoms
Therefore,
5.86 × 10⁻⁴ mol of copper contains = 5.86 × 10⁻⁴ × 6.022 × 10²³ atoms.
or
5.86 × 10⁻⁴ mol of copper contains = 35.88 × 10¹⁹ atoms
Now,
A neutral copper atom has 29 electrons.
Therefore,
Number of electrons in ball = 29 × 35.88 × 10¹⁹ = 1023.37 × 10¹⁹ electrons.
Hence,
The fraction of electrons removed = [tex]\frac{25\times10^{10}}{1023.37\times10^{19}}[/tex]
or
The fraction of electrons removed = 0.02442 × 10⁻⁹
