Nobel laureate Richard Feynman (1918-1988) once said that if two persons stood at arm's length from each other and each person had 1% more electrons than protons, the force of repulsion between them would be enough to lift a "weight" equal to that of the entire Earth. Carry out an order-of-magnitude calculation to substantiate this assertion.
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To substantiate Richard Feynman's assertion, we can perform an order-of-magnitude calculation to estimate the force of repulsion between two individuals with a 1% excess of electrons over protons.
First, let's identify the key variables and quantities involved in the calculation:
1. Number of electrons and protons per person: Assuming an average person has around 10^28 electrons and protons.
2. Distance between the two people: Taking arm's length to be around 1 meter (which is approximate and may vary).
Now, let's break down the calculation step-by-step:
1. Calculating the charge of one electron (e): The charge of an electron is approximately 1.6 x 10^-19 coulombs (C).
2. Calculating the total charge of excess electrons per person: We assume a person has 1% more electrons than protons. For 10^28 particles, this equates to 1.01 x 10^28 electrons in excess.
Total charge = (1.01 x 10^28 electrons) x (1.6 x 10^-19 C/electron)
3. Calculating the total force of repulsion between the two people: The electrostatic force between two charged objects is given by Coulomb's Law:
Force = (k x q1 x q2) / r^2
Where:
k is Coulomb's constant, approximately equal to 9 x 10^9 Nm^2/C^2
q1 and q2 are the charges of the two people (excess electrons)
r is the distance between them (1 meter)
Plugging the values into the equation:
Force = (9 x 10^9 Nm^2/C^2) x [(1.01 x 10^28 electrons x 1.6 x 10^-19 C/electron)^2] / (1 meter)^2
4. Simplifying the equation:
Force = (9 x 10^9 Nm^2/C^2) x [(1.01 x 1.6 x 10^9)^2] N
Force ≈ 2.6 x 10^23 N
Finally, let's compare this force to the weight of the Earth:
Mass of Earth ≈ 5.98 x 10^24 kg (kilograms)
Acceleration due to gravity (g) ≈ 9.8 m/s^2
Weight of Earth = Mass of Earth x g
Weight of Earth ≈ (5.98 x 10^24 kg) x (9.8 m/s^2)
Weight of Earth ≈ 5.87 x 10^25 N
The calculated force of repulsion (2.6 x 10^23 N) is significantly smaller than the weight of the Earth (5.87 x 10^25 N). Hence, Feynman's statement does not hold true based on this order-of-magnitude calculation.