Spectrum of hydrogen atom - Structure of matter

Question 1

Explain the different energy states of electron in the hydrogen atom.

Answer 1

A higher energy level of electron than that which corresponds to the ground state is not stable and a fast transition into a lower or directly into the ground state occurs with simulatneous emission of a photon.

If the state changes from energy Ek to energy En, k>n, then according to equation E₀ = - (me⁴) / (8ε²₀h²) * 1/n² , quantum of radiation is emitted with energy.

E = E_k - E_n = m_ee⁴/(32π²ε²₀ћ²) * ((1/n²) - (1/k²))

The frequency or wavelength of this readiation is given by equation E = hf = (hc)/λ, if the value of energy is substituted from the above equation.

Since there are discrete values of electron energies, only certain energyies (frequencies, wavelengths) may be emitted by the atom.

Therefore, a line spectum of radiation is observed.

Question 2

What is a series?

Answer 2

The set of spectral lines observed during reansitions from all higher levels into a vertain energy level corresponding to the given n is called the series.

Emaission spectral lines of hydroven atom, which correspond to the transition into the basic energy level (with n=1) are observed in the ultraviolet region of light and form the Lyman’s series.

The Balmer’s series corresponds to transitions into the level corresponding to n=2 and only this series can be observed within the region of visible light.

The serioes corresponding to n=3 (Paschen’s series) and to higher values of n are within the resion of infrared light.

Thus the highest energy emitted due to transition from n=infinity into the basic state with n=1 will be according to the equation.

E = E_k - E_n = m_ee⁴/(32π²ε²₀ћ²) * ((1/n²) - (1/k²))

Wavelength = 92nm.

See further equation in book - top of p.16

Question 3

Explain Balmer’s series.

Answer 3

Analogously, the highest energy in the Balmer’s series (n=2) is:

3.38eV (see full equation in book - p.16).

Its wavelength is 368nm, which already reaches the region of visible light.

The set of spectral lines observed during transitions from all higher levels observed during transitions from all higher levels into a certain energy level corresponding to the given n is called series.

Emission spectral lines of hydrogen atom those correspond to the transition into the group level (with n=1) are observed in the ultraviolet region of light and from the Lyman’s series.

The Balmer’s series corresponds to transitions into the level corresponding to n=2 and only this series can be observed within the region of visible light, as it is seen in the figure (see also p.16 in book).

The series corresponding to n=3 (Paschen’s series) and to higher values of n are within the region of infrared light.

Thus the highest energy emitted due to transition from n equal to infinity into the ground state with n=1 will be according to the equation

E = E_k - E_n = m_ee⁴/(32π²ε²₀ћ²) * ((1/n²) - (1/k²))

Where E = 13.6eV

Which corresponds to the wavelength 92nm.

Analogously, the highest energy of the Balmer’s series (n=2) is:

3.38eV

And its wavelength is:

368nm

Which already reaches the region of visible light.