Energy levels in atoms 

From Bohr’s theory of the hydrogen atom, the energy levels in multielectron atoms could not be predicted. However, the fundamental ideas of Bohr’s theory that the angular momentum of the electron has quantum (discrete) values and that energy levels of the atom have only allowed separated values which characterize the atom were valid. So, it is supposed that a given atom has a series of discrete energy levels E₀, E₁, E₂ and that no intermediate energy level systems in this state are in stable equilibrium.

Energy levels in an atom

Source: www.freesvg.org 

The ionization energy, E_i is the energy required to remove an electron completely from an atom in its most stable state.

Note: the energy received from the bombarding electron: E_n – E₀ = 6.7eV.

Wavelength of the light emitted: V= hc / ∆

And the excitation potential: E= eV

The Franck and Hertz experiment

In 1914, James Franck and Guslav Hertz found a direct experimental evidence of the existence of atomic energy levels. They studied the motion of electrons through Mercury vapour under the action of Electric field.

Franck and Hertz experiment

Source: www.en.wikipedia.org

Franck and Hertz graph showing the characteristics of current and voltage

Source: www.commons.wikimedia.org 

Types of Spectra

There are two main types of Spectra:

1. emission Spectra – where light is given out by a source; 
2. absorption Spectra – where light from a source is absorbed when it passes through another material, usually a gas or a liquid.

(C) Photoelectric effect and the quantum theory

In order for us to understand the Photoelectric effect, we have to look into the quantum theory proposed by Max Planck in 1900. This states that radiation is emitted in quanta or packets of energy. The energy, E, of a quantum of radiation is given by: E=hf. Where h is the Planck’s constant and f is the frequency of radiation, h= 6.62×10^-34Js. From experiments, it has been found that only quanta of sufficient energy and hence of sufficient high frequency would produce Photoelectric emission from a metal surface. The maximum energy, E₀, required to remove an electron from the metal surface can be written as: E₀ =hf₀ and this is known as the work function (¢) of the metal. Therefore, K.E_max =½ mv²_max =hf-¢ and from equation

K.E_max = ½ mv²_max = ½ mv²_max =eV₀ 

(D) Thermionic emission

Thermionic emission is the emission of free electrons from a hot metal surface. The energy required to cause this emission varies from metal to metal.

Diagram 1

Photocell: photocells are used in photometry, in industrial control, counting operations and in television. 

Source: www.flickr.com 

(E) X-ray production

Source: www.sites.google.com 

E_x-ray = hf = hc/∆ =eV

Uses of X-rays

1. They are used in the detection of broken bones or a tooth cavity and with the addition of iodine, x-ray are used to check respiratory or digestive disorders.
2. It is used for the treatment of malignant cancers and tumors.
3. Doses of X-rays for medical purposes to patients should be controlled as they can damage living tissues.
4. X-rays diffraction can be used in determining atomic spacing in crystals.

Past questions

1.The energy of a photon having a wavelength of 10^-10m is ? (Jamb 2013)

A. 2.0×10^-15J

B. 1.7×10^-13J

C. 2.0×10^-12J

D. 1.7×10^_12J

(h=6.63×10^-34Js c=3.0×10⁸ms^-1)

Answer: A

Source: E= hc/∆ = 6.63×10^-34×3×10^{18 /} 10^-10

              = 2×10^-15J

2. In a common emitter configuration, the output voltage is through the? (Jamb 2014)

A. Base

B. Collector

C. Emitter

D. Resistor

Answer: A

3. The production of pure spectrum could easily be achieved using a ? (Jamb 2015)

A. Triangular prism only

B. Triangular prism with two concave lenses

C. Glass prism with a pin

D. Triangular prism with two convex lenses

Answer: D

4.If the threshold frequency for tungsten is 1.3×10¹⁵Hz, what is its work function? (Jamb 2011)

A. 8.58×10^-17J

 B. 8.85×10^-18J

 C. 8.58×10^-19J

D. 8.58×10^-15J [h=6.6×10^-34Js]

Answer: C

Solution: W=hf =6.6×10^-34×1.3×10¹⁵

                   =8.58×10^-19

5.State two conditions under which photo-electrons can be emitted from the surface of a metal. (Wassce 2014)

Answer:

(i) In the presence of light

(ii) In a dark room before being exposed to ultraviolet radiation

6. Defined ionization potential? (Wassce 2013)

Answer: ionization potential or energy is the energy required to remove completely an electron from its atom.

7. List four uses of X-rays other than in medicine. (Wassce 2012)

Answer:

(i) It can be used to detect alterations which have been made on works of art.

(ii) They are used in industry to detect cracks and flaws in metals casting and welded joints.

(iii) They are also used as analytical tool for investigating crystal structure

(iv) They are used in airports to detect metals and contrabands in baggage.

8.Which of the following properties is not applicable to X-rays? They. (Wassce 2011)

A. Travel in straight lines

B. Travel with speed of light

C. Are deflected by magnetic field

D. Affect photographic films

Answer: C