Determione of the lines in the balmer series of the hydrogen atom emission spectrum is at 397 nm. it results from a transition from an upper energy level to n=2. what is the principal quantum number of the upper level? ne the initial energy level, ninitial from which the electron in the hydrogen relaxed from to the final energy level, nfinal , 4, if the emitted light has a frequency equal to 74 x 1012 (1/sec). is this wavelength in the visible region of the electromagnetic spectrum?

a)n =7 , b) n = 5

Explanation:

The energy levels of the hydrogen atom is described by the Bohr model

        = - 13.606   1/n²

This equation energy is given in elector volts and n is an integer

A transition occurs when the electro sees from a superior to a lower state

       E₀ - = -13.606 (1/² - 1/n₀²)

Let's apply this expression

         n₀ = 2

Let's look for the energy of the different levels and subtract it

n₀           (eV)

1            -13,606

2            -3.4015

3           - 1.5118

4           -0.850375

5           -0.54424

6           -0.3779

7           -0.2777

The wavelength of the transition is 397 nm = 397 10⁻⁹ m

The speed of light is related to wavelength and frequency

       c = λ f

The Planck equation gives the energy of a transition

      E = h f

      E = h c /λ

Let's calculate

     E = 6.63 10⁻³⁴ 3 10⁸/397 10⁻⁹

     E = 5.01 10⁻¹⁹ J

Let's reduce to eV

     E = 5.01 10⁻¹⁹ J (1 eV / 1.6 10⁻¹⁹ J)

     E = 3.1313 eV

Let's examine the possible transitions from the initial level ni = 2

     ΔE = - = -3.1313

     En = 3.13 -3.4015

      = 0.2702 eV

When examining the table we see that the level that this energy has is the level of n = 7

Part B      the transition is in the infrared

The frequency is 74 10¹² Hz

We use the Planck equation

       E = h f

       E = 6.63 10⁻³⁴ 74 10¹²

       E = 4.9062 10⁻²⁰ J

       E = 4.9062 10⁻²⁰ / 1.6 10⁻¹⁹

       E = 0.3066 eV

We look for the level with the energy difference

     ΔE = E₄- = 0.3066

      = 0.3066 - 0.85037

      = -0.54376 eV

When examining the table this energy has the level n = 5, therefore from this level the transition occurs

if they have a finite resultant

see earlier answer