If the gravitational force between the electron (of mass 9.11 × 10−31 kg) and the proton (of mass 1.67 × 10−27 kg) in a hydrogen atom is 1.5 × 10−47 N, how far apart are the two par- ticles? The universal gravitational constant is 6.673 × 10−11 N · m2/kg2. Answer in units of m.

r = 8.23•10^-11 m

Explanation:

Gravitational force is calculated with Newton's equation:

Fg = G•m1•m2/r²

Here, we are given values:

Fg=1.5•10^-47

G = 6.673•10^-11

m1=9.11•10^-31

m2=1.67•10^-27

r (distance) = ?

We now only need to plug these values in and solve for r:

r²= m1•m2•G/F

r²= 9.11•10^-31 • 1.67•10^-27 • 6.673•10^-11 / 1.5•10^-47

r² = 67.7 • 10^-22

r = 8.23•10^-11 m

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