Physics · Chemistry

Atomic Structure and Spectra

113 Questions

Atomic structure and spectra questions cover the Bohr model, quantum numbers, and electron transition calculations. These topics are fundamental to the physics and chemistry syllabi of competitive exams. Solving these builds confidence in handling atomic physics problems.

Bohr atomic modelHydrogen spectrum seriesElectron binding energyQuantum numbersDe Broglie wavelength

Atomic Structure and Spectra Questions

Multiple choice physics quantum physics photons concept of photon photons and photoelectric effect

The energy of a hydrogen-like atom (or ion ) in its ground state is - 122.4 eV. It may be :

  1. hydrogen atom
  2. $He^{+}$
  3. $Li^{2+}$
  4. $Be^{3+}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The ground state energy of a hydrogen-like ion is E = -13.6 * Z^2 eV. Setting -13.6 * Z^2 = -122.4, we get Z^2 = 9, so Z = 3. The element with atomic number 3 is Lithium (Li^2+).

Multiple choice physics quantum physics photons concept of photon photons and photoelectric effect

A photon of energy 12.75 eV is completely absorbed by a hydrogen atom initially in the ground state. The quantum number of the excited state is:

  1. $2$
  2. $3$
  3. $4$
  4. $5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The energy levels of hydrogen are E_n = -13.6/n^2. The energy required to reach state n from ground state (n=1) is 13.6 * (1 - 1/n^2). Setting 13.6 * (1 - 1/n^2) = 12.75, we get 1 - 1/n^2 = 12.75/13.6 = 0.9375. Thus 1/n^2 = 0.0625, n^2 = 16, n = 4.

Multiple choice physics quantum physics photons concept of photon photons and photoelectric effect

A 14 eV energy photon ionises a hydrogen atom in its lowest energy level. The kinetic energy of the electron ejected from the atom will be :

  1. 14 eV

  2. 13.6 eV

  3. 27.6 eV

  4. 0.4 eV
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Ionization energy of hydrogen is 13.6 eV. If a 14 eV photon is absorbed, the excess energy becomes the kinetic energy of the ejected electron. K = 14 - 13.6 = 0.4 eV.

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

In a laboratory experiment on emission from atomic hydrogen in a discharge tube, only a small number of lines are observed where as a lines are present in the hydrogen spectrum of a star. This is because in a laboratory  

  1. The amount of hydrogen taken is much smaller than that present in the star

  2. The temperature of hydrogen is much smaller than that of the star

  3. The pressure of hydrogen is much smaller than that of the star

  4. The gravitational pull is much larger than that in the star
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a laboratory discharge tube, the low pressure of hydrogen gas limits the number of collisions and the population of excited states, resulting in fewer observed spectral lines compared to the high-pressure, high-temperature environment of a star.

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

Ionization energy of $Li$(Lithium) atom in ground state in $5.4 eV$. Binding energy of an electron in $Li^+$ ion in ground state is $75.6 eV$. Energy required to remove all three electrons of Lithium (Li) atom is:-

  1. $203.4 \ eV$
  2. $135.4 \ eV$
  3. $81.0 \ eV$
  4. $156.6 \ eV$
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

Find the  binding energy of a H atom in the state n = 2

  1. 2.1 eV

  2. 3.4 eV

  3. 4.2 eV

  4. 2.8 eV
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The energy levels of a hydrogen atom are given by E_n = -13.6 / n^2 eV. For n = 2, E_2 = -13.6 / 4 = -3.4 eV. The binding energy is the magnitude of this energy, which is 3.4 eV.

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

If the energy of an electron in Hydrogen atom is given by expression, $-1312 /{ n }^{ 2 }kJ{ mol }^{ -1 }$, then the energy required to excite the electron from ground state to second orbit is 

  1. $328 kJ{ mol }^{ -1 }$
  2. $656 kJ{ mol }^{ -1 }$
  3. $984 kJ{ mol }^{ -1 }$
  4. $1312 kJ{ mol }^{ -1 }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\begin{array}{l} E=-1312\left( { \frac { 1 }{ 4 } -1 } \right)  \ =\frac { { -1312\times 3 } }{ 4 }  \ =328\times 3 \ =984\, kJmo{ l^{ -1 } } \ Hence, \ option\, \, C\, \, is\, \, correct\, answer. \end{array}$

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

The rest energy of an electron is

  1. $510 KeV$
  2. $931 KeV$
  3. $510 MeV$
  4. $931 MeV$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rest energy of an electron $=m _{ e }{ c }^{ 2 }$
Here $m _{ e }=9.1\times { 10 }^{ -31 }kg$ and $C$ = velocity of light

$\therefore$ Rest energy $=9.1\times { 10 }^{ -31 }\times\left( 3\times { 10 }^{ 8 } \right) ^{ 2 }joule$

                         $=\displaystyle \frac { 9.1\times { 10 }^{ -31 }\times \left( 3\times { 10 }^{ 8 } \right) ^{ 2 } }{ 1.6\times { 10 }^{ -19 } } eV\simeq 510KeV$

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

The energy equivalent of $1\ amu$ is

  1. $931\ eV$
  2. $93.1\ V$
  3. $931\ MeV$
  4. $9.31\ MeV$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$1\ amu =1.66\times 10^{-27} kg$


According to Einstein's mass energy equivalence, $E=mc^2$ where $c=$ velocity of light. 

So, $E=1.66\times 10^{-27}\times (3\times 10^8)^2=14.94\times 10^{-11} J$

$E=\dfrac{14.94\times 10^{-11}}{1.6\times 10^{-19}} eV$       where $1eV=1.6\times 10^{-19} J$

$E=931\times 10^{6} eV=931\ MeV$

Multiple choice chemistry nuclear physics nuclear reactor the nuclear power station isotopes and nuclear chemistry

What is the order of the temperature at which average kinetic energy of an atom in gaseous hydrogen becomes equal to the binding energy of the electron in hydrogen atom?

  1. $10^{4}$ K
  2. $10^{5}$ K
  3. $10^{3}$ K
  4. $10^{2}$ K
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the temperature be $T$.

So, the K.E. of an atom is gaseous hydrogen is $3kT/2$
where $k=1.38\times10^{-23}$ is the boltzmann constant.
Now the binding energy of the electron in hydrogen atom is $13.6eV=13.6\times1.6\times10^{-19}\ J$
Equating Binding energy and the kinetic energy we get, 
$T=1.004\times10^5\ K$
So temperature is of order of $10^5\ K$

Multiple choice chemistry matter in our surroundings diffusion in different states of matter properties of solids, liquid, and gas particle theory of matter

The helium atom is two times heavier than a hydrogen molecule. At $298$ K, the average kinetic energy of a helium atom is:

  1. Two times that of hydrogen molecule

  2. Same as that of a hydrogen molecules

  3. Four times that of a hydrogen molecules

  4. Half that of a hydrogen molecule
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the formula of average kinetic energy:


$K.E. = \dfrac 32 KT$

K.E does not depend upon mass.


$\therefore$ At the same temperature, K.E will be same.

Hence, option $B$ is correct.

Multiple choice collisions in one dimension collisions work, energy and power mechanics physics

A free hydrogen atom in ground state is at rest. A neutron of kinetic energy $K$ collides with the hydrogen atom. After collision hydrogen atom emits two photons in succession one of which has energy $2.55\ eV.$
(Assume that the hydrogen atom and neutron has same mass)

  1. Minimum value of $K$ is $25.5\ eV.$
  2. Minimum value of $K$ is $12.75\ eV.$
  3. The other photon has energy $10.2\ eV$ if $K$ is minimum.
  4. The upper energy level is of excitation energy $12.75\ eV$.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To excite the atom to the n=3 level (energy -1.51 eV from -13.6 eV), the energy required is 12.09 eV. If it emits a 2.55 eV photon (n=3 to n=2), the remaining energy must be 10.2 eV (n=2 to n=1). The minimum energy K must account for the excitation and the recoil energy of the atom.

Multiple choice physics electromagnetic waves properties and uses of different radiation electromagnetic spectrum spectrum

Hydrogen atom does not emit X-rays because

  1. it contains only a single electron

  2. energy levels in it are far apart

  3. its size is very small

  4. energy levels in it are very close to each other
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Hydrogen is the least energetic element. Even the most energetic line that hydrogen emits (when an electron drops down from the second shell to the first) has only enough energy to be an ultraviolet photon. This is because the energy levels in hydrogen atom are very close. So hydrogen atoms do not emit X rays.

Multiple choice

The Bohr model of the atom describes the electrons in an atom as orbiting the nucleus in discrete, quantized energy levels. Which of the following energy levels is the lowest?

  1. n = 1

  2. n = 2

  3. n = 3

  4. n = 4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The lowest energy level in the Bohr model is n = 1, which corresponds to the electron being closest to the nucleus.

Multiple choice

What is the Born-Oppenheimer approximation?

  1. An approximation that separates the electronic and nuclear motions in a molecule

  2. An approximation that neglects the interactions between electrons in a molecule

  3. An approximation that assumes that the electrons in a molecule are independent of each other

  4. An approximation that assumes that the nuclei in a molecule are fixed in space
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Born-Oppenheimer approximation is an approximation that separates the electronic and nuclear motions in a molecule. It assumes that the electrons move much faster than the nuclei, so that the electronic wave function can be calculated for a fixed nuclear configuration.