KPK Board 12th class Physics Ch 19 Atomic Spectra short questions answers

When energy is supplied to hydrogen atom, it will be excited and its single electron will jump from its ground state to some higher energy level. Now, when the atom is de-excited, the electron from higher energy level returns to the ground state by several jumps. Therefore, spectral lines of different wavelength are emitted. That is why the spectrum of hydrogen contains many lines, although its atom contains a signal electron.

If we suppose that the electron in hydrogen atom obey the classical mechanics, then we would have to observe continuous spectrum. Because according to classical electromagnetic theory a constantly accelerating charge emit energy continuously in the form of electromagnetic waves. An electron moving in an orbit around the nucleus also has the acceleration in its motion.

a = V²/r

So a constantly accelerating electron should radiate energy continuously. Thus classical model predicts a continuous spectrum of such a hypothetical hydrogen atom which is contrary to the discrete line spectrum observed in the laboratory.

Yes the electron can absorb a photon of energy 13.6eV or greater than 13.6ev in the ground state.

13. Less than 13.6eV: The absorption of photon by an atom is a resonance phenomenon. So when a photon of energy less than 13.6 but exactly equal the citation energy such as 10.2eV, 12.75eV, 13.056 V, 13.22eV etc is absorbed by atom. The atom is raised to excited state but soon it returns to ground state by emitting photon of the same energy.
14. Greater than 13.6eV: Since the ionization energy of the electron in the ground state of hydrogen atom is 13.6eV. So when a photon of energy greater 13.6eV is incident on the electron in the ground state of hydrogen atom, it is absorbed and ionization of the atom takes place. The energy 13.6eV is used to eject the electron from the atom and set free, while the surplus energy is taken by the electron as K.E. If the energy of photon is exactly equal to 13.6V, then ionization will take place but K.E of the electron will be zero.

1. Solids: Solids give rise to continues spectra because in solids the atoms are not free but so strongly packed that their orbits overlap. There for in solids the atoms can be raised to the excited state only when the substance is heated. When a solid is heated the electrons from outer most orbits are to positive states. The transition takes place between +ve energy states. When emitted radiations are introduced to a spectrometer, a continuous spectrum is observed in which contains every wavelength over a broad region laboratory.

2.Gases: In gases the atoms are isolated and free. There are distinct orbits (-ve + energy states) which are available for transition. In gases the atoms are raised to the excited states by the method of L direct collision between the electrons of the atom & other electrons, ions or atoms this can be done by electric discharge through the gas. When these excited atoms come to the ground state radiations are emitted. The spectra of these radiations consist of a number of narrow bright lines which is due to the transitions of individual atoms. Each line has its own wavelength which is the characteristic of the element.

The differences between laser light and light from an electric bulb are given below.

Laser light: Laser light is monochromatic, which consists of a single wavelength. Laser light is phase coherent, i.e light waves are in the same phase. Laser light is unidirectional. It moves in the same direction. Laser light is produced due to stimulated emission of radiation. Laser light is more intense than  the ordinary light.

Light from an electric lamp: The ordinary light from electric bulb has a number of wavelengths. The ordinary light of an electric bulb has no phase coherence. Here the light waves are out of phase. Light emits from an electric bulb in all directions. It spreads out as it moves away from the lamp. The electric bulb light is produced due to spontaneous emission of radiation. The intensity of bulb light is less than the laser light.

When classical electromagnetic theory failed to explain Rutherford nucleus atom where positive charges are concentrated in the central part of the atom called nucleus and electrons are moving in orbits around the nucleus, like our solar system. In 1913 Neil Bohr extended Plank’s quantum theory to Rutherford nuclear atom and proposed a model of an atom. Bohr assumed that a constantly accelerating electron around the nucleus does not radiate energy. The total energy of the electron in one of its allowed orbit remains constant. The energy is emitted when an electron jumps from higher orbit to lower energy state.

On account of greater charge number Z the helium atom ₂H⁴e has greater ionization energy. Helium (₂H⁴e ) atom has two protons in the nucleus due to which the coulomb attractive force on an electron is doubled as compare to hydrogen.

F = Ke.2e/r²_n = 2Ke²/r²_n

1 Le than the

The K.E and PE of electron in nth orbit of Helium atom are double than the hydrogen. Calculating the total energy of electrons in the lowest orbit of helium atom is, 4 times greater than the energy of electron in Hydrogen.

(E_n) Helium = – 4[ 4π²K²e⁴m/n²h²]

(E₁) Hel = -4(E̥)

(E₁)He = -4(13.6) = -54.4eV

Therefore the ionization energy of ₂H⁴e (Helium) is greater than the Hydrogen. Ionization energy of ₂H⁴e = E-E₁ =0-(-54.4) eV = 54.4eV.

1. X-rays are very short wavelength (10m) electromagnetic radiations. The characteristic described in the question shows the dual nature of x-rays. When x- rays fall on a metal surface, electrons are emitted from the metal surface and the process is known as photoelectric effect. Here x-rays photons behaves as particles and eject electrons, when incident on a metal surface. The K.E of photoelectron is:

K.E = hf – φ

KE = hf – hf̥

2. The diffraction of x-rays by crystal such rock salt (NaCl) shows the wave nature. As diffraction is the most important application of the X-rays to study the structure of crystals. The diffraction and interference effects are the best evidences to prove the wave nature of the X-rays. The diffraction of X-rays obeys Braggs Law which is given by:

2d sin θ = mλ

X-ray has some different properties from light on account of high frequency and short wavelength. X-rays are very short wavelength (10″ “m) and high frequency electromagnetic radiations. They can be reflected, refracted, diffracted and polarized like ordinary light waves. They are similar in nature to ordinary light. Therefore x-rays possess similar properties, specific to light waves. But even though due to short wavelength and high frequency X-rays have different properties.

1. For example x-rays cannot be diffracted by diffraction grating or double slits experiments. They can be diffracted by crystal and obey Brag’s law.
2. X-rays have high penetrating power than light.
3. In addition to characteristic line x-rays spectrum, there has been observed another continuous X-ray spectrum.

A laser is a device which emits a very narrow intense beam of laser light hay the following properties.

1. Laser bean is monochromatic. It consist the photons of only one wavelength Therefore all the photons of the beam will have the same frequency and the same color light.
2. The laser beam is coherent i.e. the crests and troughs of the beam are in the same phase.
3. The laser beam is unidirectional i.e. the radiations of the beam travel in the same direction. Thus laser beam travels in the same direction. Thus laser beam is a very intense, unidirectional monochromatic and coherent beam of visible light.

A high intense monochromatic beam of laser is used as a laser knife. Laser knife are used for various purposes. Laser knives are widely used in medical surgery. In surgery laser knives has proved a more delicates instrument than the finest scalpel. It has been used for bloodlessly removing small tumors, cuttings etc. It is also used to fragment gall stone and kidney stones. Laser beam can be used for welding of detached retina to the eye. Laser knife is a small weapon which creates a small beam of light scalpel. It has been use energy from its hit like miniature, light saber. There are records of this weapon being used in the underground of railway system.

We cannot see atom because the size of an individual atom is smaller than the wavelength of light.

Explanation: In fact we can see only those objects whose size is larger than the wavelength of the visible light rays reflecting from that object. Now the radius of atom exists between 46 x 10^-15 to 221 x 10^-15 meters while the wavelength of visible light is of the order of 10^-6m. Thus the wavelength of visible light is longer when the size of an atom. The atom is so small that it cannot be seen by visible or even by X-rays. Thus we use electron microscope to see an atom which uses a beam of electron whose wavelength is smaller than the size of atom.

The radiation being produced by a beam of decelerated charged particles is called breaking radiation or Bremsstrahlung which means slowing-down radiation. In addition to characteristics X-rays spectrum, there has been observed another continuous X-rays spectrum. This can be explained on the basis of classical theory, according to which an accelerated charged particle emits electromagnetic radiation. When a fast moving electron in X-ray tube, strikes a target T, the force of attraction between electron and the nucleus of an atom accelerates the motion of electron and changes its path as shown. This high K.E electron when strike the target atom is slowed and strongly decelerated. This decelerated electron emits electromagnetic radiation of energy hf, which is called X-rays. In this case if the electron loses its whole energy eV and is transferred to the energy of X-ray photon hf_max then we have.

eV = hf_max

C = λ_max f_max

f_max = C/ λ_max

eV = hC/ λ_max

Hence λ_max  correspond to f_max

λ_max = hC/ eV

The process in which atoms of a substance are raised from ground state E1, to the excited state E3 is optical pumping. The operation of laser depends upon the existence of Meta stable state in the atoms of some substances. Consider a material whose raised from the ground state E₁ to the excited state E₃ with incident photons energy hf₁₃ = E₃ – E₁. This process is called optical pumping. The atoms in excited state E₃ do not decay back to state E₁, because such transitions a forbidden by the selection rules as shown. On the other hand the atoms in the excited state E₃ whose mean life is 10^-8 second, decay spontaneously to state E₂. The life time of state E₂ is 3×10^-3 second which is much longer than 10^-8 sec. Thus the atoms reach E₂ much faster than they leave the state E₂. Therefore state E₂ is known as metastable state. This leads to increase number of atoms in state E₂ as compare to the number of atoms in state E₁. so E₁ < E₂. so N₂ <N₁. This means that population inversion has archived. This process is known as optical pumping.