Energy Levels

Q.

The shortest wavelength for the Lyman series is $912A^{\circ }$. Find the shortest wavelength for Paschen and Brackett series in the Hydrogen atom.

Q.

Consider the reaction $C{r}_2{O}_{\mathit{7}}^{\mathit{2}\mathit{-}}+14H^{+}+6e^{-}\to 2C{r}^{3+}+7H_{2}O$. What is the quantity of electricity in coulombs needed to reduce $1$ mol of $C{r}_2{O}_{\mathit{7}}^{\mathit{2}\mathit{-}}$?

1. $6\times {10}^6\mathrm{C}$

2. $5.79\times {10}^5\mathrm{C}$

3. $5.25\mathrm{x}{10}^5\mathrm{C}$

4. None of these

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

Q. The longest wavelength in Lyman series of hydrogen atom spectrum corresponding to $H_{\alpha }$ line is approximately.

1. $1218\stackrel{\circ }{A}$
2. $216\stackrel{\circ }{A}$
3. $6578\stackrel{\circ }{A}$
4. $1016\stackrel{\circ }{A}$

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

Q.

The potential energy$\left(\mathrm{U}\right)$ of a diatomic molecule is a function dependent on r (interatomic distance) as $\mathrm{U}=\frac{\mathrm{\alpha }}{{\mathrm{r}}^{10}}-\frac{\mathrm{\beta }}{{\mathrm{r}}^5}-3$. Where, $\mathrm{a}$ and $\mathrm{b}$ are positive constants. The equilibrium distance between two atoms will ${\left(\frac{2\mathrm{\alpha }}{\mathrm{\beta }}\right)}^{\raisebox{1ex}{$\mathrm{a}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{b}$}\right.}$. Where $\mathrm{a}$ =_______

Q. Ratio of the wavelengths of first line of Lyman series and first line of Balmer series is

1. 1 : 3
2. 27 : 5
3. 5 : 27
4. 4 : 9

Q. The total energy of an electron in the first excited state of the hydrogen atom is about –3.4 eV. (a) What is the kinetic energy of the electron in this state? (b) What is the potential energy of the electron in this state? (c) Which of the answers above would change if the choice of the zero of potential energy is changed?

Q. The transition from the state n = 3 to n = 1 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition,

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

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

Q. The ratio of the wavelengths for $2\to 1$ transition in $L{i}^{++},H{e}^{+}$ and H is

1. 1 : 2 : 3
2. 1 : 4 : 9
3. 4 : 9 : 36
4. 3 : 2 : 1

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 wavelength of the first member of Balmer series is $6563\stackrel{\circ }{A}$. Calculate the wavelength of second member of Lyman series.

1. $6563\stackrel{\circ }{A}$
2. $1025.5\stackrel{\circ }{A}$
3. None of these
4. $2025\stackrel{\circ }{A}$

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. one
3. three
4. four

Q. The electric potential between a proton and an electron is given by $V=V_{0}ln\frac{r}{r_0}$, where $r_0$ is a constant. Assuming Bohr’s model to be applicable, write variation of $r_n$ with n, n being the principal quantum number

1. $r_n\infty n$
2. $r_n\alpha \frac{1}{n}$
3. $r_n\alpha n^2$
4. $r_n\alpha \frac{1}{n^2}$

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. The third line of Balmer series of an ion equivalent to hydrogen atom has wavelength of 108.5 nm. The ground state energy of an electron of this ion will be

1. 3.4 eV
2. 13.6 eV
3. 54.4 eV
4. 122.4 eV

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. A difference of 2.3 eV separates two energy levels in an atom. Whatis the frequency of radiation emitted when the atom make atransition from the upper level to the lower level?

Q.

In a hydrogen discharge tube, it is observed that through a given cross-section $3.13\times {10}^{15}$ electrons are moving per second from right to left and $3.12\times {10}^{15}$ protons are moving from left to right per second. The electric current in the discharge tube and its direction will be

1. $1.6\mu A$ towards left

2. $1mA$ towards right

3. $1.6\mu A$ towards right

4. $1mA$ towards left

Q.

Calculate the shortest and longest wavelengths in the hydrogen spectrum of the Lyman series.

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. The ratio of the frequencies of the longest wavelength limits of the Lyman and Balmer series of hydrogen is respectively:

1. 27:5
2. 5:27
3. 4:1
4. 1:4

Q. A single electron orbits a stationary nucleus of charge +Ze, where Z is a constant. It requires 47.2 eV to excite an electron from second Bohr orbit to third Bohr orbit. Find the value of Z

1. 2
2. 5
3. 3
4. 4

Q.

Which element has the highest binding energy?

Q. A hydrogen - like atoms has one electron revolving around a stationary nucleus. The energy required to excite the electron from the second orbit to the third orbit is 47.2 eV. The atomic number of the atom is:

1. 3
2. 4
3. 5
4. 6

Q. Every series of hydrogen spectrum has an upper and lower limit in wavelength. The spectral series which has an upper limit of wavelength equal to $18752\stackrel{\circ }{A}$ is

1. Balmer series
2. Lyman series
3. Paschen series
4. Pfund series