Question

If the gravitational force between the electron (9.11 ✕ 10-31 kg) and the proton (1.67 ✕ 10-27 kg) in a hydrogen atom is 1.26 ✕ 10-47 n, how far apart are the two particles?

Answer 1

F = gravitational force between electron and proton = 1.26 x 10⁻⁴⁷ N

m = mass of proton = 1.67 x 10⁻²⁷ kg

M = mass of the electron = 9.11 x 10⁻³¹ kg

r = distance between electron and proton = ?

G = universal gravitational constant = 6.67 x 10⁻¹¹

gravitational force between electron and proton is given as

F = G M m/r²

inserting the values

(1.26 x 10⁻⁴⁷) = (6.67 x 10⁻¹¹) (1.67 x 10⁻²⁷) (9.11 x 10⁻³¹)/r²

r = 8.97 x 10⁻¹¹ m

Answer 2

Gravitational force is given by the formula

`F_g = (Gm_1m_2)/(r^2)`

here we know that

`F_g = 1.26 * 10^(-47)N`

`m_1 = 9.11 * 10^(-31) kg`

`m_2 = 1.67 * 10^(-27) kg`

now we will plug in all values in above equation

`F_g = ((6.67 * 10^(-11))(9.11 * 10^(-31))(1.67 * 10^(-27)))/(r^2)`

now solving for distance "r" between them

`r = 8.97 * 10^(-11) m`

so above is the distance between them