Calculate the orbital period

Therefore, the final equation would be: Number of Orbits = (1.0*10^-8 s * (3*10^8 m/s)/ (2π*(3.42*10^-16 m)^2). In summary, to calculate the orbital period in each level (n=1, 2, 3) using the Bohr model, you can use equations (4), (1), and (5). For the average lifetime of the first excited level, you need to calculate the number of orbits using the circumference and speed of the electron.
  • #1
Firben
145
0
1)Use the bohr model, calculate the orbital period in eachlevel(n=1,2,3)

2) the average lifetime of the first excited level of a hydrogen atom is 1.0 10^-8 s. In the bohr model, how many orbits does an electron in the n=2 level complete before returning to the ground level?



Homework Equations



E(n) = -13.60/(n^2) (1)
λ = hc/(E(2)-E(1)) (2)
f = c/λ (3)
f = (E(1)-E(2))/h (4)
T = 1/f (5)
h = 6.626*10^-31 J*s
r(n) = ε(n^2*h^2)/(π*m*e^2) (6)
m=9.109*10^-19 kg
ε(0) = 8.85 * 10^-12 C^2/N*m^2
e = 1.60*10^-19 C

The Attempt at a Solution



After i have numerically inserted the values in the equations (4),(1) and (5) i got i to be
3.42*10^-16 s, 3.2466*10^-16s and 4.10*10^-16 is that correct ?

In 2) should i calculate circumference to begin with ?
 
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  • #2
For the second part, you need to calculate the circumference of the orbit using equation (6), and then use the average lifetime of the first excited level to calculate the number of orbits that the electron completes before returning to the ground state. The equation you need is: Number of Orbits = (Average Lifetime * Speed of Electron) / Circumference where Speed of Electron = c/2π and Circumference = 2πr(n).
 

1. What is the formula for calculating orbital period?

The formula for calculating orbital period is T=2*pi*sqrt(a^3/GM), where T is the orbital period in seconds, a is the distance between the two objects in meters, G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), and M is the mass of the central object in kilograms.

2. How do I determine the distance between two objects for the orbital period calculation?

To determine the distance between two objects, you can use the distance formula (d=√(x2-x1)^2+(y2-y1)^2), where x and y are the coordinates of the two objects in a two-dimensional plane. If you are working with three-dimensional coordinates, you can use the distance formula for three dimensions (d=√(x2-x1)^2+(y2-y1)^2+(z2-z1)^2).

3. What units should I use for the orbital period calculation?

The units for orbital period are typically seconds, but they can also be expressed in minutes, hours, or days depending on the scale of the objects and their orbital period. It is important to ensure that all units used in the calculation are consistent to get an accurate result.

4. Can the orbital period be calculated for any type of orbit?

Yes, the orbital period formula can be used to calculate the orbital period for any type of orbit, as long as the distance between the two objects and the mass of the central object are known. This includes circular, elliptical, and parabolic orbits.

5. How accurate is the orbital period calculation?

The orbital period calculation using the formula mentioned above is highly accurate, as long as the input values are precise. However, factors such as gravitational pull from other objects and external forces can affect the actual orbital period of an object, so the calculated value may not always match the observed period exactly.

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