If your body develops a charge of -17 (microcoulombs), how many excess electrons has it acquired, and what is their collective mass?
Q = -17*10^-6 Coulombs
electron is -1.6 * 10^-19 Coulombs/electron
so
-17*10^-6 *(-1/1.6) * 10^19
= 10.6 * 10^13 electrons
multiply that by 9.1*10^-31 kg/electron to get kilograms if you need grams instead multiply by 10^3 again
12
To determine the number of excess electrons acquired by the body, we can use the equation:
Q = ne
Where:
Q is the total charge in coulombs,
n is the number of excess electrons, and
e is the charge of a single electron (1.6 x 10^-19 C).
Given that the body has a charge of -17 microcoulombs (-17 × 10^-6 C), let's calculate the number of excess electrons:
Q = ne
-17 × 10^-6 C = n × (1.6 × 10^-19 C)
To find the number of excess electrons (n), divide both sides of the equation by the charge of a single electron:
n = (-17 × 10^-6 C) / (1.6 × 10^-19 C)
n ≈ -1.06 × 10^13 electrons
Therefore, the body has acquired approximately 1.06 × 10^13 excess electrons (negative charge).
Now, let's calculate the collective mass of these excess electrons. The mass of a single electron is approximately 9.1 × 10^-31 kg.
The collective mass of electrons (m) can be calculated using the equation:
m = n × me
Where:
m is the collective mass of electrons,
n is the number of excess electrons, and
me is the mass of a single electron.
m = (-1.06 × 10^13) × (9.1 × 10^-31 kg)
m ≈ -9.646 × 10^-18 kg
Therefore, the collective mass of the excess electrons is approximately -9.646 × 10^-18 kg (negative mass).
To determine the number of excess electrons and their collective mass, we need to use the elementary charge and the electron mass.
1. Determine the charge on a single electron:
The elementary charge, symbolized as "e," is the fundamental unit of electric charge and is approximately equal to -1.602 × 10^-19 coulombs.
Therefore, the charge on a single electron is -1.602 × 10^-19 C.
2. Calculate the number of excess electrons:
Since your body has a charge of -17 microcoulombs, we can divide this value by the charge on a single electron to find the number of excess electrons.
Number of excess electrons = (-17 × 10^-6 C) / (-1.602 × 10^-19 C)
Simplifying this equation, we find:
Number of excess electrons = 1.061 × 10^13 electrons
Therefore, your body has acquired approximately 1.061 × 10^13 excess electrons.
3. Calculate the collective mass of the excess electrons:
The mass of an individual electron, symbolized as "m_e," is approximately equal to 9.10938356 × 10^-31 kilograms.
To find the collective mass of the excess electrons, we multiply the mass of a single electron by the number of excess electrons:
Collective mass = (1.061 × 10^13 electrons) × (9.10938356 × 10^-31 kg/electron)
Simplifying this equation, we find:
Collective mass ≈ 9.654 × 10^-18 kg
Therefore, the collective mass of the excess electrons is approximately 9.654 × 10^-18 kilograms.