In the Bohr model of the hydrogen atom, an electron in the 2nd excited state moves at a speed of 5.48X10^5 m/s in a circular path having a radius of 2.12X10^-10 m. What is the effective current associated with this orbiting electron?
T= 2πR/v,
I=e/T=ev/2πR=
=1.6•10⁻¹⁹•5.48•10⁵/2•π•2.12•10⁻¹º=
=6.58•10⁻⁵A
To calculate the effective current associated with the orbiting electron in the 2nd excited state of the hydrogen atom, you can use the formula for electric current:
I = q * v / t
Where:
I is the electric current,
q is the charge of the electron,
v is the speed of the electron,
and t is the time it takes for the electron to complete one orbit.
In the Bohr model, the time it takes for an electron to complete one orbit in a circular path is given by the equation:
t = (2 * π * r) / v
Where:
t is the time,
r is the radius of the circular path,
and v is the speed of the electron.
Let's calculate the time it takes for the electron to complete one orbit:
t = (2 * π * 2.12X10^-10 m) / (5.48X10^5 m/s)
t ≈ 2.424X10^-16 s
Now, let's calculate the effective current:
I = q * v / t
The charge of the electron, q, is approximately 1.6X10^-19 C.
I = (1.6X10^-19 C) * (5.48X10^5 m/s) / (2.424X10^-16 s)
I ≈ 3.61X10^-11 A
Therefore, the effective current associated with the orbiting electron in the 2nd excited state of the hydrogen atom is approximately 3.61X10^-11 Amperes.
To find the effective current associated with the orbiting electron in the Bohr model, we need to use the formula for the current in a circular path, which is given by:
I = q * v / (2πr),
where I is the current, q is the charge, v is the velocity, and r is the radius of the circular path.
In this case, we are dealing with the hydrogen atom, where the charge of the electron is given by the elementary charge, e = 1.6x10^-19 C.
Substituting the values into the formula, we have:
I = (1.6x10^-19 C) * (5.48x10^5 m/s) / (2π * 2.12x10^-10 m).
Now, let's calculate this value:
I = (1.6x10^-19 C) * (5.48x10^5 m/s) / (2π * 2.12x10^-10 m).
Using a calculator, we find that:
I ≈ 2.44x10^5 A.
Therefore, the effective current associated with this orbiting electron in the Bohr model is approximately 2.44x10^5 Amperes.