Question

Part A.

What is the magnitude of the force between a proton and an electron separated by a distance of 1μm?

Answers: 2.3 x 10 ^(-16)

Part b

Compare this force to the weight of a 0.200-mg flea due to Earth's gravity. (Select the correct answer)

A. The flea's weight is ~10^8 (one hundred million times) greater than the attraction between the 1μm separated charges.

B. The flea's weight is ~10^{12} (one trillion times) greater than the attraction between the 1μm separated charges.

C. The flea's weight is ~100 (one hundred times) greater than the attraction between the 1μm separated charges.

D. The flea's weight is ~10,000 (ten thousand times) greater than the attraction between the 1μm separated charges.

E. The flea's weight is approximately the same as the attraction between the 1-\muμm separated charges.

F. The flea's weight is ~10^{10} (ten billion times) greater than the attraction between the 1μm separated charges.

Part c

If the distance between the proton and electron were reduced by a factor of 1000-times, so that they were separated by a mere 1 nm (about the length of a single glucose molecule); how would the attraction between the charges compare to the weight of the 200-μg flea?

(Select the correct answer)

A) The flea's weight is ~10^8 (one hundred million times) greater than the attraction between the 1-μm separated charges.

B) The flea's weight is ~10^{12} (one trillion times) greater than the attraction between the 1-μm separated charges.

C) The flea's weight is ~100 (one hundred times) greater than the attraction between the 1-μm separated charges.

D) The flea's weight is ~10,000(ten thousand times) greater than the attraction between the 1-μm separated charges.

E) The flea's weight is approximately the same as the attraction between the 1-\muμm separated charges.

F) The flea's weight is ~10^{10} (ten billion times) greater than the attraction between the 1-μm separated charges.

Answer 1

Electrostatic force is given by:

Fe = k*q1*q2/r^2

q1 = +e

q2 = -e

r = 1*10^-6 m

So,

Fe = 9*10^9*(1.6*10^-19)^2/(1*10^-6)^2

Fe = 2.30*10^-16 N

2.

Force due to gravity will be:

Fg = m*g

m = mass of flea = 0.200 mg = 0.200*10^-6 kg

g = 9.8 m/sec^2

So,

Fg = 0.200*10^-6*9.8

Fg = 1.96*10^-6 N

So,

Fg/Fe = 1.96*10^-6/(2.30*10^-16) = 8.5*10^9

Fg = 0.85*10^10*Fe

So The flea's weight is ~10^{10} (ten billion times) greater than the attraction between the 1μm separated charges.

Correct option is F.

3.

Please check your question again OR ask your instructor, as in the part c question distance between proton and electron is mentioned as 1 nm, while in the given options distance between them is 1 $\mu$ m. I'm solving it according to options.

when distance between proton and electron = 1 nm = 1*10^-9 m

then

Fe = 9*10^9*(1.6*10^-19)^2/(1*10^-9)^2

Fe = 2.30*10^-10 N

when mass of flea = 200 $\mu$ g = 200*10^-9 kg

Fg = 200*10^-9*9.8 = 1.96*10^-6 N

then

Fg/Fe = (1.96*10^-6)/(2.30*10^-10)= 8.5*10^3 = 0.85*10^4

Fg = 0.85*10^4*Fe = 0.85*10000*Fe

The flea's weight is ~10,000(ten thousand times) greater than the attraction between the 1-μm separated charges.

Correct option is D.

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