Whats the speed of an electron of Bohr's orbit K
v(n) = ℏn/m•r = e²/4•π•ε₀•ℏ•n=
=v₁/n=2.19•10⁶/n m/s
n=1 v₁=2.19•10⁶ m/s
To find the speed of an electron in Bohr's orbit, you can use the formula:
v = (2πr) / T
Where:
- v is the speed of the electron,
- r is the radius of the orbit,
- T is the time taken to complete one revolution.
Bohr's model of the atom assumes that the electron orbits the nucleus in discrete, circular orbits. The radius of the K orbit is approximately 0.0529 nanometers.
To calculate the time taken to complete one revolution (T), we use the formula:
T = (2πr) / v₀
Where:
- v₀ is the velocity of the electron in the first Bohr orbit.
- v₀ is given by v₀ = Ze² / (2πε₀mr₀), where Z is the atomic number, e is the elementary charge, ε₀ is the vacuum permittivity, m is the electron's mass, and r₀ is the Bohr radius.
For the electron in the first Bohr orbit (K orbit), Z = 1, e is approximately 1.602 x 10^-19 coulombs, ε₀ is approximately 8.854 x 10^-12 farads per meter, m is the electron mass (9.10938356 x 10^-31 kilograms), and r₀ is approximately 0.529 x 10^-10 meters.
Now, we can substitute the values into the formula to calculate v₀:
v₀ = (1 x (1.602 x 10^-19)²) / (2π x (8.854 x 10^-12) x (9.10938356 x 10^-31) x (0.529 x 10^-10))
After calculating v₀, you can substitute the obtained value along with the radius (r) into the speed formula to find the speed of the electron in the K orbit.