Question

The mass of an electron is 9.11 x 10^-31 kg. The mass of a proton is 1.67 x 10^-27 kg. They are about 1.0 x 10^-10 m apart in a hydrogen atom. What is the gravitational force between these two particles in the hydrogen atom?

A) 1.07 x 10^-36 N
B) 5.18 x 10^-10 N
C) 1.01 x 10^-7 N
D) 2.43 x 10^-7 N

Answer 1

The gravitational force between an electron and a proton in a hydrogen atom can be calculated using Newton's law of universal gravitation with given mass and distance values, resulting in a force of approximately 1.07 x 10^-36 N.

Step-by-step explanation:

The question asks about the gravitational force between an electron and a proton within a hydrogen atom. To calculate this, we use Newton's law of universal gravitation, which is given by the formula:

F = G (m1 * m2) / r^2

where F is the gravitational force, G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), m1 and m2 are the masses of the two objects (in this case, the electron and proton), and r is the distance between the centers of the two masses.

Plugging in the given values (m1 = 9.11 x 10^-31 kg for the electron, m2 = 1.67 x 10^-27 kg for the proton, and r = 1.0 x 10^-10 m), we find:

F = (6.67 x 10^-11 Nm^2/kg^2) * (9.11 x 10^-31 kg) * (1.67 x 10^-27 kg) / (1.0 x 10^-10 m)^2

After calculating the above expression, you get a force of approximately 1.07 x 10^-36 N, which corresponds to option A).