In the hydrogen atom, the distance between the electron and the proton is 5x10^-11m.
a)Compute the magnitude of the gravitational force FG between the electron and the proton
b)Compute the magnitude of the electrical force FE between the electron and the proton
c)How many times larger in magnitude is FE than FG?
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F(gravitation)=G(M1M2)÷r^2
G(gravitational constant)=6.61×10^-11
To compute the magnitude of the gravitational force FG between the electron and the proton, we can use Newton's law of universal gravitation. The formula is:
FG = (G * m1 * m2) / r^2
Where:
- FG is the gravitational force
- G is the gravitational constant (6.67430 × 10^-11 N * m^2 / kg^2)
- m1 and m2 are the masses of the two objects (proton and electron in this case)
- r is the distance between the two objects
In this case, we assume the mass of the proton is approximately 1.67 × 10^-27 kg, and the mass of the electron is approximately 9.11 × 10^-31 kg. The distance between them is given as 5 × 10^-11 m.
a) To compute FG, we substitute the values into the formula:
FG = (6.67430 × 10^-11 N * m^2 / kg^2) * (1.67 × 10^-27 kg) * (9.11 × 10^-31 kg) / (5 × 10^-11 m)^2
b) To compute the magnitude of the electrical force FE between the electron and the proton, we can use Coulomb's law. The formula is:
FE = (k * |q1 * q2|) / r^2
Where:
- FE is the electrical force
- k is the Coulomb's constant (8.9876 × 10^9 N * m^2 / C^2)
- q1 and q2 are the charges of the two objects (proton and electron in this case)
- r is the distance between the two objects
In this case, the charge of the proton is +1.602 × 10^-19 C, and the charge of the electron is -1.602 × 10^-19 C.
b) To compute FE, we substitute the values into the formula:
FE = (8.9876 × 10^9 N * m^2 / C^2) * (|1.602 × 10^-19 C * -1.602 × 10^-19 C|) / (5 × 10^-11 m)^2
c) To find how many times larger in magnitude FE is than FG, we can divide FE by FG:
FE / FG
To summarize:
a) Compute FG using the formula FG = (G * m1 * m2) / r^2
b) Compute FE using the formula FE = (k * |q1 * q2|) / r^2
c) Compute the ratio FE / FG.