To make a large-scale representation of a hydrogen atom in its ground state, you start with a super ball (D=3.78 cm) to represent the nucleus. How far away, R, in km will you have to put the representation electron?
To determine the distance, R, in kilometers to place the representation electron, we will need to use the concept of atomic radius and convert the given sizes to the appropriate units.
1. Start by converting the diameter of the super ball in centimeters (cm) to meters (m) by dividing by 100:
Diameter (m) = 3.78 cm / 100 = 0.0378 m
2. Next, we need to find the atomic radius of the hydrogen atom in its ground state. The atomic radius can vary depending on the reference source; however, a common estimate for the atomic radius of hydrogen is around 0.053 nm.
Convert the atomic radius from nanometers (nm) to meters (m) by dividing by 10^9:
Atomic radius (m) = 0.053 nm / 10^9 = 5.3 x 10^-11 m
3. Now that we have the diameter of the super ball and the atomic radius of the hydrogen atom both in meters, we can calculate the distance, R, in meters using the formula:
R = Radius of the super ball + Atomic radius of the hydrogen atom
R = (0.0378 m / 2) + 5.3 x 10^-11 m
4. Finally, convert the distance, R, from meters (m) to kilometers (km) by dividing by 1000:
R (km) = R (m) / 1000
Inserting the values and solving the equation, we get:
R = (0.0378 / 2) + 5.3 x 10^-11 = 1.9 x 10^-2 m (approximately)
R (km) = 1.9 x 10^-2 m / 1000 = 1.9 x 10^-5 km (approximately)
Therefore, you will have to place the representation electron approximately 1.9 x 10^-5 km away from the super ball nucleus to create a large-scale representation of a hydrogen atom in its ground state.