Energy Levels

Q.

How do you calculate the ionization energy $(\mathrm{in}\mathrm{kJ}{\mathrm{mol}}^{-1})$ of the ${\mathrm{He}}^{+}$ ion?

Q. A doubly ionized Lithium atom is like a hydrogen atom with atomic number 3. What is the wavelength of the radiation required to excite the electron from first to third Bohr's orbit?

1. $11114\stackrel{\circ }{A}$
2. $114\stackrel{\circ }{A}$
3. $14\stackrel{\circ }{A}$
4. $4\stackrel{\circ }{A}$

Q.

The transition from the state n = 4 to n = 3 in a hydrogen-like atom results in ultra violet radiation. Infrared radiation will be obtained in the transition. (IIT-JEE-2001)

1. $2\to 1$
2. $3\to 2$
3. $4\to 2$
4. $5\to 4$

Q. Energy E of a hydrogen atom with principal quantum number n is given by $E=\frac{-13.6}{n^2}eV$. The energy of a photon
ejected when the electron jumps n = 3 state to n = 2 state of hydrogen is approximately

1. 1.9 eV
2. 1.5 eV
3. 0.85 eV
4. 3.4 eV

Q.

What is the harmonic series in math?

Q. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy $12.1eV$. According to Bohr's theory, the spectral lines emitted by hydrogen will be

1. two
2. three
3. four
4. one

Q. Energy levels A, B, C of an atom are shown below


If $E_A<E_B<E_C$, the wavelength emitted due to transistion from C to A is ${\lambda }_3$then correct statements of the following is

1. ${\lambda }_3={\lambda }_1+{\lambda }_2$
2. ${\lambda }_3=\frac{{\lambda }_1\times {\lambda }_2}{{\lambda }_2+{\lambda }_1}$
3. ${\lambda }_1+{\lambda }_2+{\lambda }_3=0$
4. ${\lambda }_3^2={\lambda }_1^2+{\lambda }_2^2$

Q. How many different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are excited to states with principal quantum number n?

1. $\frac{n^2}{2}$
2. $\frac{(n-1{)}^2}{2}$
3. $\frac{n(n-1)}{2}$
4. $\frac{\left(n\right(n-1){)}^2}{2}$

Q. Transitions between three energy levels in a particular atom give rise to three spectral lines of wavelengths, in increasing magnitudes, ${\lambda }_1,{\lambda }_2$ and ${\lambda }_3$. Which one of the following equations correctly relates ${\lambda }_1,{\lambda }_2$, and ${\lambda }_3$?

1. ${\lambda }_1={\lambda }_2-{\lambda }_3$
2. ${\lambda }_1={\lambda }_3-{\lambda }_2$
3. $\frac{1}{{\lambda }_1}=\frac{1}{{\lambda }_2}+\frac{1}{{\lambda }_3}$
4. $\frac{1}{{\lambda }_1}=\frac{1}{{\lambda }_3}-\frac{1}{{\lambda }_2}$

Q. The ionization potential of the hydrogen atom is 13.6 eV. Its energy in n = 2 energy state is

1. -3.4 eV
2. -6.8 eV
3. -13.6 eV
4. - 27 .2 eV

Q. The energy required to take the electron from second orbit to third orbit of hydrogen atom is approximately

1. $48.5eV$
2. $10.2eV$
3. $1.9eV$
4. $13.6eV$

Q. Energy of the electron in $n^{th}$ orbit of hydrogen atom is given by $E_n=-\frac{13.6}{n^2}eV$. The amount of energy needed to
transfer electron from first orbit to third orbit is

1. 13.6 eV
2. 3.4 eV
3. 12.09 eV
4. 1.51 eV

Q. A hydrogen atom in the ground state emits a photon of energy 12.1 eV. Its orbital angular momentum changes by $\Delta$L. Then $\Delta$L is equal to

1. $1.05\times {10}^{-34}Js$
2. $2.11\times {10}^{-34}Js$
3. $3.16\times {10}^{-34}Js$
4. $4.22\times {10}^{-34}Js$

Q. Transitions between three energy levels in a particular atom give rise to three spectral lines of wavelengths, in increasing magnitudes, ${\lambda }_1,{\lambda }_2$ and ${\lambda }_3$. Which one of the following equations correctly relates ${\lambda }_1,{\lambda }_2$, and ${\lambda }_3$?

1. ${\lambda }_1={\lambda }_2-{\lambda }_3$
2. ${\lambda }_1={\lambda }_3-{\lambda }_2$
3. $\frac{1}{{\lambda }_1}=\frac{1}{{\lambda }_2}+\frac{1}{{\lambda }_3}$
4. $\frac{1}{{\lambda }_1}=\frac{1}{{\lambda }_3}-\frac{1}{{\lambda }_2}$

Q. The first member of the Paschen series in hydrogen spectrum is of wavelength $18,800\stackrel{\circ }{A}$. The short wavelength limit of Paschen series is

1. $1215\stackrel{\circ }{A}$
2. $6560\stackrel{\circ }{A}$
3. $8225\stackrel{\circ }{A}$
4. $12850\stackrel{\circ }{A}$

Q. The wavelength of radiation emitted is ${\lambda }_0$ when an electron jumps from the third to the second orbit of hydrogen atom. If the electron jumps from the fourth to the second orbit of the hydrogen atom, the wavelength of radiation emitted will be

1. $\frac{16}{25}{\lambda }_0$
2. $\frac{20}{27}{\lambda }_0$
3. $\frac{27}{20}{\lambda }_0$
4. $\frac{25}{16}{\lambda }_0$

Q. A stationary hydrogen atom emits a photon corresponding to first line of Lyman series. The velocity of recoil of the atom is

1. 7.29 m/s
2. 2.79 m/s
3. 3.2 m/s
4. 5.32 m/s

Q.

To excite an electron from one orbit to another we need:

1. A photon of energy equal to the difference between the two orbits’ energies

2. A photon of any energy

3. A photon of energy equal to the energy of the higher orbit of the two

4. A photon with energy equal to the energy of the lower orbit of the two

Q. The wave number of energy emitted when electron jumps from fourth orbit to second orbit in hydrogen in 20497 $c{m}^{-1}$. The wave number of energy for the same transition in $H{e}^{+}$ is

1. $5,099c{m}^{-1}$
2. $20,497c{m}^{-1}$
3. $40,994c{m}^{-1}$
4. $81,988c{m}^{-1}$

Q. Energy levels A, B, C of an atom are shown below


If $E_A<E_B<E_C$, the wavelength emitted due to transistion from C to A is ${\lambda }_3$then correct statements of the following is

1. ${\lambda }_3={\lambda }_1+{\lambda }_2$
2. ${\lambda }_3=\frac{{\lambda }_1\times {\lambda }_2}{{\lambda }_2+{\lambda }_1}$
3. ${\lambda }_1+{\lambda }_2+{\lambda }_3=0$
4. ${\lambda }_3^2={\lambda }_1^2+{\lambda }_2^2$

Q. The ionization potential of the hydrogen atom is $13.6\text{volt}$. The energy required to remove an electron from the second orbit of hydrogen is:

1. $3.4\text{eV}$
2. $6.8\text{eV}$
3. $13.6\text{eV}$
4. $27.2\text{eV}$

Q. Hydrogen (H), deuterium (D), singly ionized helium $\left(H{e}^{+}\right)$ and doubly ionized lithium $\left(L{i}^{++}\right)$ all have one electron around the nucleus. Consider n = 2 to n = 1 transition. The wavelengths of emitted radiations are ${\lambda }_1,{\lambda }_2,{\lambda }_3$ and ${\lambda }_4$ respectively. Then approximately

1. ${\lambda }_1={\lambda }_2=4{\lambda }_3=9{\lambda }_4$
2. $4{\lambda }_1=2{\lambda }_2=2{\lambda }_3={\lambda }_4$
3. ${\lambda }_1=2{\lambda }_2=2\sqrt{2{\lambda }_3}=3\sqrt{2{\lambda }_4}$
4. ${\lambda }_1={\lambda }_2=2{\lambda }_3=3{\lambda }_4$

Q.

To excite an electron from one orbit to another we need:

1. A photon of energy equal to the difference between the two orbits’ energies

2. A photon of any energy

3. A photon of energy equal to the energy of the higher orbit of the two

4. A photon with energy equal to the energy of the lower orbit of the two

Q. If the wavelength of the photon emitted due to transition of an electron from the third orbit to the first orbit in a hydrogen atom is $\lambda$, then the wavelength of photon emitted due to transition of an electron from the fourth orbit to the second orbit will be

1. $\frac{128}{27}\lambda$
2. $\frac{25}{9}\lambda$
3. $\frac{36}{7}\lambda$
4. $\frac{125}{11}\lambda$

Q. Say, you observe a heated gaseous sample of $L{i}^{++}$ atoms, knowing that all the electrons are in the third Bohr orbits. How many spectral lines will you find in the emission spectrum of this sample?

1. Infinitely many - it will be a continuous spectrum
2. 3
3. 5
4. 1

Q. The transition from the state n = 4 to n = 3 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from :

1. $3\to 2$
2. $4\to 2$
3. $5\to 4$
4. $2\to 1$

Q. If the wavelength of first member of Balmer series of hydrogen spectrum is $6564\dot{A}$, the wavelength of second member of Balmer series will be:

1. $1215\dot{A}$
2. $4862\dot{A}$
3. $6050\dot{A}$
4. $5892\dot{A}$

Q. As $n$ increases, the difference in energy level keeps increasing. Where $n$ is the principal quantum number.

1. True
2. False

Q. In the $n^{th}$ orbit, the energy of an electron $E_n=-\frac{13.6}{n^2}eV$ for hydrogen atom. The energy required to take the electron from first orbit to second orbit will be

1. 10.2 eV
2. 12.1 eV
3. 13.6 eV
4. 3.4 eV

Q. The energy levels of a certain atom for 1st, 2nd and 3rd levels are E, $\frac{4E}{3}$ and 2E respectively. A photon of wavelength $\lambda$ is emitted for a transition $3\to 1$. What will be the wavelength of emissions for transition $2\to 1$

1. $\frac{\lambda }{3}$
2. $\frac{4\lambda }{3}$
3. $\frac{3\lambda }{4}$
4. $3\lambda$