Atomic Spectra
EXERCISE
MULTIPLE CHOICE QUESTIONS
Choose the best possible answer:
1. Which of the following series of hydrogen spectra lies in the visible region of the spectrum?
A. Layman
B. Balmer
C. Paschen
D. Bracket
2. The longest wavelength in Balmer's series with wavelength is 656.2 nm corresponds to
A. n = 3
B. n = 4
C. n ^ prime =5
D. n = ∞
3.If 13.6 eV energy is required to ionize the hydrogen atom, then the required energy to remove an electron from n = 2i
A. 10.2 eV
B. O eV
C. 3.4 eV
D. 6.8 eV
4. If an atom exists in excited state n = 5 the maximum number of transitions
that take place is
A. 3
B. 5
C. 10
D. 25
5. The energy of the electron in the excited state * n = 4 in hydrogen atom is
A.-13.6 eV
B.-3.4 eV
c - 0.85 eV
D. - 1.5eV
6.The radius of third Bohr orbit is greater than the radius of first Bohr orbit (Bohr's radius) by factor of
A. 3
B. 6
C. 9
D. 16
7. The reverse process of X-ray production can be related to
A. Compton Effect
B. Photoelectric Effect
C. Pair Production
D. Pair Annihilation
8.The duration of meta-stable state is approximately
A. 10-³ s
B. 10 ^ - 6 * s
C. 10 ^ 8 * s .
D. 10 ^ - 10 * s
9. Helium-Neon Laser beam emitted from a discharge tube has a color
A. Blue
B. Green
C. Red
D. White
10. In He-Ne LASER, the discharged tube is filled with
A. 50% He & 50% Ne
B. 15% He & 85% Ne
C. 85% He & 15% Ne
D. 99% He & 1% Ne
11. In neon, the 20.66-eV level can undergo lasing action to the 18.70-eV level. What is the energy of the resulting photons?
A. 20.66 eV
B. 18.70 eV
C. 39.36 eV
D. 1.96 eV
12. In connection with inner shell transition the symbol Lp refers to x-ray emission associated with an electron going from
A. n = 3 n = 1
B. n = 4 to n = 1
D. n = 5 n = 3
C. n = 4 n = 2
13. In laser the pumping is performed to
A. produce meta-stable states
B. produce stimulated emission
C. achieve population inversion
D. achieve coherency in photons
14. Linear momentum of an electron in Bohr orbit of H-atom (principal quantum number n) is proportional to:
A. n
B. 1/n
C. n²
D. 1/n²
CONCEPTUAL QUESTIONS
1. Why does the spectrum of hydrogen consist of many lines even though a hydrogen atom has only a single electron?
Ans. There are many quantized orbits around the nucleus to which electron in the hydrogen atom can be excited. Due to these different levels of excitation, the cor responding de excitations show different line spectra in the spectrum of hydrogen. Explanation: The multiple lines in the hydrogen atomic spectrum are not pro duced by single atom, having only one electron. The sample of hydrogen gas that produces this spectrum contains different atoms that were excited to different energy levels.Many lines in the spectrum are result of the transitions in different atom, return from higher energy state to the ground state of the sample. In some cases, the electron may also return to the ground state by making several transitions. Conclusion: Thus, the spectrum of hydrogen atom has many different lines, even the hydrogen atom contains only one electron.
2. Why do solids give rise to continuous spectrum while hot gases give rise toline spectrum?
Ans. Since in solids, the atoms and molecules are close together, due to which it gives rise to continuous spectrum. While in gases, atoms or molecules are far from one another, which results in a line spectrum. Explanation: In solids atoms are not free but they are packed so tightly that their orbits overlap with each other. The energy changes in a particular atom are im pacted by the other atoms in the surrounding. The impact is the radiations of all wavelengths are emitted. Therefore, solids give rise to continuous spectra. On the other hand, atoms of the hot gases are isolated and far apart from one another. No atom of the gas influences the other atoms, and hence, radiations of specific wavelengths and frequencies are emitted. Therefore, hot gases give riseto line spectra.
3. Can the electron in the ground state of hydrogen absorb a photon of energy (a) less than 13.6 eV (b) greater than 13.6 eV?
Ans. Yes, the electron in the ground state of hydrogen can absorb a photon of energy both less than 13.6 eV as well as greater than 13.6 eV. For Photon having energy less than 13.6 eV: The electron can absorb a photon of energy less than 13.6 eV by making a transition to some intermediate state such as one with n = 2. The energy of an electron in the ground state is -13.6 eV. The next energy level greater than that is -3.4 eV. So, for a ground state electron to move into a higher energy state the photon it absorbs must have energy of 10.2 eV. Since the electron cannot go into a state between -13.6 eV and -3.4 eV, it will not absorb a photon having energy less than 13.6 eV and greater than 10.2 eV: Hence for a photon having energy less than 13.6 eV to be absorbed by the electron in the ground state of hydrogen atom, it must have energy equal to the energy difference between the two allowed states of the hydrogen atom. Such that;
2.17×10-18
J 13.6eV
E n²
n²
For Photon having energy greater than 13.6 eV: It can also absorb a photon of energy greater than 13.6 eV, but in doing so, the electron would be separated from the atom and the excess energy (over 13.6 eV) will be carried by electron as its kinetic energy.
Conclusion: Therefore, electron in the ground state of hydrogen absorbs a photon of energy both less than 13.6 eV as well as greater than 13.6 eV. But with a re striction that photon energy less than 13.6 eV, must be equal to the energy differ ence between the allowed states.
4. Why do the spectral lines in the hydrogen atom become closer together farther away from the nucleus?
Ans. The spectral lines in the hydrogen atom become closer together because as the energy levels get higher, the wavelengths become smaller and so is their difference. Thus, the levels get closer together. Explanation: The lines in the spectrum of the hydrogen atom are caused by an electron moving from a higher energy level to a lower energy level. Light is emitted in that process. The shorter the wavelength of the light emitted, the greater its energy. Also, the lines in a particular series get closer together because difference in the wavelength of two consecutive lines decreases.
Example: Consider the spectrum of Lyman series (the spectrum obtained by the de-excitation of electron from higher shells to the 1st shell is known as Lyman series).
The wavelengths of the lines in these series can be calculated by the empirical
Missing Formula
From Eq. (1), Eq. (2) and Eq. (3), it is clear that the difference in wavelength be tween Ly-ẞ and Ly-a is greater than the difference in Ly-y and Ly-ẞ. Conclusion: Therefore; it is concluded that as the energy level gets higher, the difference in the wavelength of two consecutive lines decreases, and that is the reason that spectral lines are getting closer to one another.
5. Why it was necessary to quantize angular momentum in Bohr's model of the atom?
Ans. The quantization of angular momentum in Bohr's model of the atom was necessary for the justification of quantized orbits.
Explanation: After the failure of Rutherford atomic model, and to explain the line spectrum of Hydrogen gas, Bohr made a very bold assumption that as long as an electron is orbiting the nucleus in a certain orbit, it neither emit nor absorb energy. Whenever an electron makes a transition from higher orbit to lower orbit, it emits energy in the form of photon. In order to explain the formation of line spectrum, Bohr introduced the concept of quantized stationary (stable) orbits. It was only made possible by considering the angular momentum to be quantized.
Therefore, in 2nd postulate, Bohr state that only those orbits are allowed for which the angular momentum is integral multiple of h/2r.
Mathematically:
h
mvr=n
Where, rn is the quantized orbit and n is the principal quantum number. Conclusion: Thus, in order to justify the concept of quantized orbits, it was neces sary to quantized angular momentum in Bohr's model of the atom.
6. Why X-rays have different properties from light even though both originate
from orbital transition of electrons in excited atoms?
Ans. Although both X-rays and light are electromagnetic radiations and both orig inate from the orbital transition of electrons in excited atoms, still they have similar as well as different properties. Examples of the dissimilar properties of X-rays are.
1. X-rays have high penetrating power than light.
2. X-rays cannot be diffracted by Young's double slits apparatus or a diffraction grating.
3. X-rays exhibit line as well as continuous spectra.
The differences in the properties are attributed to the difference in the wave length and frequencies of X-rays and light. X-rays are originated from the inner shells transitions and having short wavelengths and high frequencies as compared to visible light.
7. If the potential difference in an x-ray tube is increased, how does this affect the wavelengths of (a) bremsstrahlung x-rays and (b) characteristic x-rays?
Ans. X-rays are generated via interactions of the accelerated electrons with elec trons of tungsten nuclei within the tube anode. There are two types of X-rays gen erated; bremsstrahlung or continuous radiation and characteristic radiation.
(a) Bremsstrahlung x-rays: This is also known as continues x-rays. Since the minimum wavelength (cutoff wavelength) is given by; hc
The equation reveals that if potential difference of an x-ray tube is increased, then the wavelength of the x-rays is decreased. Conclusion: The wavelength of continuous x-rays produced depends on potential difference of x-ray tube and is independent of target atom. But the target atom should be heavier atom like cobalt, tungsten. (b) Characteristic x-rays: Characteristic x-rays are emitted when a high energy electron knocks out an inner shell electron of the target atom and another elec tron (in atom) makes a transition from a high energy state to a low energy state to fill the vacancy. For example, in Ka x-rays are emitted when electron makes transition from the high energy state (L shell) to the K shell of the atom. So, wave length of x-rays depends on energy difference of orbits from where electron is jumping.
Conclusion: The wavelength of characteristic x-rays is independent of the poten tial difference of x-ray tube but depends on target atom.
8. Crystal lattices can be examined with x-rays but not UV. Why?
Ans. Crystal lattices can be examined with x-rays but not with UV, because wave length of x-rays is much smaller than UV and is of the order of interplanar distance of crystal lattice.
Explanation: Both x-rays and UV (ultraviolet) are electromagnetic waves; the x rays, typically, with a wavelength of 0.01nm to 10 nm, while the UV, typically, with a wavelength of 10 nm to 400 nm.
For diffraction the necessary condition is that the wavelength should be compa rable to the width of the slits. Since in crystals the interplanar distance is of the order of wavelength of x-rays, therefore x-rays are diffracted through crystals, whereas UV wavelengths are much larger than lattice spacings in crystals and can not be diffracted.
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