According to Bohr's theory, what is the frequency of the light emitted by an electron in a transition from the first excited state to the ground state in hydrogen? Compare this with the frequency of the orbital motion of the electron in the first excited state.

frequency transition 2.4626 10¹⁵ Hz

Explanation:

Bohr's atomic model works very well for the hydrogen atom, the energy of the states is described by the expression

En = - 13.606 / n² eV

Where n is a positive integer

Let's calculate the energy for the base state n = 1 E1 = - 13.606 eV

The energy for the first excited state n = 2 E2 = - 13.6060 / 2²

E2 = - 3.4015 Ev

The variation of the energy for the transition is

ΔE = E2 - E1

ΔE = - 3.4015 + 13.606

ΔE = 10.2045 eV

We use the Planck equation to find the frequency

E = 10.2045 eV (1.6 10⁻¹⁹ J/1 eV) = 16.3272 10⁻¹⁹ J

E = h f

f = E / h

f = 16.3272 10⁻¹⁹ / 6.63 10⁻³⁴

f = 2.4626 10¹⁵ Hz

Let's calculate the frequency of the excited state

E2 = 3.4015 eV (1.6 10⁻¹⁹ J/1eV) = 5.4424 10⁻¹⁹ J

f = 5.4424 10⁻¹⁹ / 6.63 10⁻³⁴

f = 0.8209 10¹⁵ Hz

To make the comparison, divide the two frequencies

f transition / f excited = 2.4626 / 0.8209

f transition / f excited = 3

The frequency of the transition is 3 times greater than the frequency of the first excited state