Bihar Board - Class 12 Physics - Chapter 12: Atoms Short Answer Question

1. Define impact parameter.

Answer:- Impact parameter of an alpha particle is defined as the perpendicular distance of the velocity vector of α-particle from the central line of the gold nucleus, when it is far away from the gold nucleus.

2.  What is the scattering angle if impact parameter (b) Has a zero value?

Answer:- If impact parameter b is zero, then the angle of scattering, θ = 180° or π rad.

3. What force is responsible for an α-particle scattering?

Answer:- The electrostatic repulsive force between the nucleus of gold and the alpha particle is responsible for an α-particle scattering.

4. What is the main feature of Rutherford's nuclear atom model?

Answer:- Rutherford's atom is an electrically neutral sphere consisting of a very small massive and positively charged nucleus at the center surrounded by revolving electrons in their respective orbits. The requisite centripetal force for orbital motion of electrons is provided by coulombic attractive force between nucleus and the revolving electron.

5. Explain how Rutherford's experiment on scattering of α-particles led to the estimation of the size of the nucleus.

Answer:- By experimental studies of large angle scattering of α-particles, the value of the distance of the closest approach (r0) for α- particles was determined. The size of the nucleus can be either less than or equal to the distance of the closest approach. Thus, the distance of the closest approach provides us with an upper limit of the size of the nucleus. In this way, the size of the nucleus was estimated. The estimated size of the nucleus is of the order of 10-14 m.

6.  State Bohr's postulate of quantisation of angular momentum of the election in hydrogen atoms.

Answer:- As per the Bohr's postulate, the electron revolves around the nucleus only in those orbits for which angular momentum of the electron is some integer multiple of h/2n, where h is the universal Planck's constant.

Mathematically,

                                   mvnrn=nh2                         where n = 1, 2, 3, ...

7.  What is Bohr's radius? What is its value?

Answer:- Bohr's radius is the size (radius) of the innermost orbit of an electron in its ground state (n = 1) for a hydrogen atom. Its value is 5.29 x 10-11 m (~5.3 × 10-11 m).

8.  Define ionization energy. What is its value for a hydrogen atom?

Answer:- The minimum amount of energy required to free the valence electron from its ground state in an atom is called 'ionization energy' for that atom/element. Ionization energy of hydrogen is +13.6 eV.

9.  How are ionization energy and ionization potential interrelated?

Answer:- Numerical value of ionization energy of an atom expressed electron volts is equal to the ionization potential for the atom. As an example, ionization energy for a hydrogen atom is 13.6 eV and its ionizing potential is 13.6 V.

10.  What do you mean by Hα, Hβ, Hγ, ... lines of hydrogen spectrum?

Answer:- The first, second, third,... lines of the Balmer series of hydrogen spectrum are generally termed as Hα, Hβ, Hγ, ... lines.

11. What are hydrogenic atoms? Give examples too.

Answer:- Hydrogenic atoms are the atoms consisting of a nucleus with positive charge +Ze and a single electron, where Z = proton number (atomic number) of the nucleus. Hydrogen atoms (H), singly ionized helium (He+), doubly ionized lithium (Li++), etc., are the examples of hydrogenic atoms.

12.  How can you say that most of an atom is empty?

Answer:- The size of an atom is of the order of (10-10 - 10-11 m) and the size of a nucleus is of the order of (10-14 - 10-15 m). Outside the nucleus, there are only a few electrons orbiting around the nucleus. It conclusively proves that most of an atom is empty. Again, it is due to this reason that most α-particles pass without any deviation in Rutherford's α-particles scattering experiment.

13.  What is the significance of negative energy of the orbiting electron in an atom?

Answer:- The negative energy of an orbiting electron of an atom signifies that the electron is bound to the nucleus and the force between them is attractive in nature.

14.  Why is the idea of stationary states very important in Bohr's atom model?

Answer:- Bohr atom is stable only on account of the concept of stationary state/orbit.

15.  Bohr assumed that the nucleus is fixed. Was this assumption correct? If not, what is the error in Bohr's predicted values for frequencies of the spectral lines?

Answer:- Truly speaking, the nucleus of an atom is not fixed. When energy is emitted due to electronic transition from one energy state to another, there is recoil motion of the nucleus too. However, as the mass of the nucleus is extremely large as compared to the mass of electrons, the recoil speed of the nucleus is very small and may be neglected. Therefore, practically, the nucleus may be considered to be stationary.

16.  How does the atomic spectrum differ from a continuous spectrum?

Answer:- A continuous spectrum (e.g., spectrum of white sunlight) consists of lines of all possible wavelengths/frequencies, without any break, spread over a large region. However, an atomic gas or vapor, on proper excitation, emits radiation containing certain specific wavelengths only. Such a spectrum is termed a line atomic spectrum.

17.  What is the difference between emission spectrum and absorption spectrum of an atomic gas?

Answer:- When an atomic gas is excited at low pressure, the emitted radiation is emission line spectrum which consists of bright lines on a dark background. Each bright line corresponds to a particular frequency/ wavelength.

When white light passes through an atomic gas and the transmitted light is analyzed, some dark lines are observed in the spectrum. These dark lines correspond to those very wavelengths, which were found in the emission spectrum of the gas. This type of spectrum consisting of intermittent dark lines in white light spectrum is called the line absorption spectrum of the material of the gas.

18.  What would happen if the electrons in an atom were stationary?

Answer:- If electrons in an atom were stationary, they would be pulled into the nucleus on account of coulombic attractive force. Such an atom would not be a stable atom.

19. How does an atom remain stable in which the electron is revolving around the nucleus in a definite orbit?

Answer:- If the electron is revolving around the nucleus in a definite orbit in the atom, coulombian force acting on the electron is utilized just to provide the requisite centripetal force and the electron continues to revolve in the same orbit with a constant orbital speed. Thus, the atom will be stable provided that the electron is revolving in a nonradiating orbit (i.e., it does not emit radiation while revolving in its orbit.)

20. Is frequency of radiation emitted continuous or discrete as per (a) Rutherford atom model, and (b) Bohr atom model?

Answer:- (a) As per Rutherford atom model, the frequency of radiation emitted by an atom is continuous and exactly equal to the revolution frequency of the electron of the atom.

(b) As per Bohr atom model, the frequencies of radiation emitted are discrete. The radiation frequency is equal to the difference between the energies in two states (initial and final) of electrons divided by Planck's constant h.

21. Although a hydrogen atom has only one electron yet its spectrum has many lines. Explain why.

Answer:- According to the Bohr atom model, emission of a radiation photon of characteristic frequency takes place whenever the electron of a hydrogen atom shifts from a higher energy excited state to another lower energy excited state or ground state. Depending upon the degree of excitation, so many transitions like (2-1), (3-2), (4-2), (4-1), etc., are possible. Each transition gives a spectral line of characteristic frequency. Thus, we obtain a large number of spectral lines in the hydrogen spectrum irrespective of the fact that it has only one electron in an atom.

22. Why does the Bohr atom model fail for multielectron atoms?

Answer:- As per Bohr atom model, we have considered electrostatic attractive force experienced by the electron due to a positively charged nucleus only. For multielectron atoms, each electron will also experience repulsive forces due to other electrons present in the atom. As the Bohr atom model does not take these repulsive forces into account, it fails to explain atomic spectra of multielectron atoms.

23. Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K). What results do you expect?

Answer:- If one uses a thin sheet of solid hydrogen in place of the gold foil in an α-particle scattering experiment, no large angle scattering of α-particles will be possible. Mass of a hydrogen nucleus (proton) is only 1.67 x 10-27 kg which is even less than that of an α-particle (ma = 6.7 x 10-27 kg). So, even in a head-on collision, the alpha particle will not bounce back. The situation is similar to a moving football colliding with a tennis ball at rest. In such a situation, one cannot expect football to bounce back without disturbing the tennis ball.

24. Why is the classical (Rutherford) model for an atom—an electron orbiting around the nucleus—not able to explain the atomic structure? 

Answer:-

As the revolving electron loses energy continuously, it must spiral inwards and eventually fall into the nucleus. So it was not able to explain the atomic structure.

25. If Bohr's quantisation postulate (angular momentum = nh2 is a basic law of nature, it should be equally valid for the case of planetary motion also. Why then do we never speak of quantisation of orbits of planets around the sun?

Answer:- If one applies Bohr's quantisation principle for planetary motion (say, Earth), then the value of principal quantum number n = 1070. For such large values of n, the difference in angular momenta and energy between successive levels is meaningless and we may consider angular momenta as well as energy levels as continuous ones.