THE DISTANCE BETWEEN 4th AND 3rd BOHR ORBITS OF He+ is ?
To calculate the distance between the 4th and 3rd Bohr orbits of He+, we can use the formula for the radius of the nth Bohr orbit:
rn = (0.529 × n^2) / Z, where
rn is the radius of the nth orbit,
n is the principal quantum number,
Z is the atomic number.
In the case of He+ (Helium ion), Z = 2 since it has lost one electron.
First, let's calculate the radius of the 4th Bohr orbit (r4) using the formula:
r4 = (0.529 × 4^2) / 2
r4 = (0.529 × 16) / 2
r4 = 8.464 Å (Ångstroms)
Next, let's calculate the radius of the 3rd Bohr orbit (r3) using the formula:
r3 = (0.529 × 3^2) / 2
r3 = (0.529 × 9) / 2
r3 = 2.37 Å (Ångstroms)
Finally, we can calculate the distance between these two orbits by finding the difference between their radii:
Distance = r4 - r3
Distance = 8.464 Å - 2.37 Å
Distance ≈ 6.094 Å (Ångstroms)
Therefore, the distance between the 4th and 3rd Bohr orbits of He+ is approximately 6.094 Å.
To find the distance between the 4th and 3rd Bohr orbits of He+, we need to use the formula for the radius of an orbit in the Bohr model.
The formula to calculate the radius of an orbit is given by:
r = n^2 * (h^2 / (4π^2 * me * ke^2)) * (1 / Z)
Where:
- r is the radius of the orbit
- n is the principal quantum number of the orbit
- h is the Planck constant (6.62607015 × 10^-34 m^2 kg / s)
- π is a constant (approximately 3.14159)
- me is the mass of the electron (9.10938356 × 10^-31 kg)
- ke is the Coulomb's constant (8.9875517923 × 10^9 N m^2 / C^2)
- Z is the atomic number of the nucleus (in this case, Z is 2 since we are dealing with He+ which has one proton)
Now let's calculate the distances between the 4th and 3rd Bohr orbits of He+:
For the 4th Bohr orbit (n = 4):
r4 = 4^2 * (h^2 / (4π^2 * me * ke^2)) * (1 / 2)
For the 3rd Bohr orbit (n = 3):
r3 = 3^2 * (h^2 / (4π^2 * me * ke^2)) * (1 / 2)
Subtracting r3 from r4 will give us the distance between these two orbits:
r4 - r3 = (4^2 * (h^2 / (4π^2 * me * ke^2)) * (1 / 2)) - (3^2 * (h^2 / (4π^2 * me * ke^2)) * (1 / 2))
Simplifying the equation further will give us the final answer.
I didn't realize that someone was teaching Bohr's model anymore, little planets circling around the nucleus.
In the Bohr model, the "radius" of orbit in the n energy state is given by
radius= 5.92e-11 (n/Z) meters Z for He is 2, put in 4, 3 and subtract to get the "distance'. However, please dont think one can measure it as a real distance.