Atomic Energy Levels

Q. Forbidden energy gap of $\text{Ge is}0.75\text{eV}$, maximum wavelength of incident radiation for producing electron-hole pair in germanium semiconductor is-
[Use $h=6.6\times {10}^{-34}\text{Js}$]

1. $4200\mathring{A}$
2. $16500\mathring{A}$
3. $4700\mathring{A}$
4. $4000\mathring{A}$

Q.

Calculate the Bohrs radius for the fifth orbit of the hydrogen atom.

Q. According to Bohr's theory of the hydrogen atom, the total energy of the hydrogen atom with its electron revolving in the $n^{th}$ stationary orbit is proportional to

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

Q. Kinetic energy of electron in first Bohr orbit is

1. 489.6 eV
2. 4.896 eV
3. 0.489 eV
4. 48.96 eV

Q. Minimum excitation potential of Bohr's first orbit in hydrogen atom is

1. $13.6\text{V}$
2. $3.4\text{V}$
3. $10.2\text{V}$
4. $3.6\text{V}$

Q. According to Bohr's theory of hydrogen atom, the product of the binding energy of the electron in the $n^{th}$ orbit and its radius in the $n^{th}$ orbit -

1. Is proportional to $n^2$
2. Is inversely proportional to $n^3$
3. Has a constant value of $-7.2\text{eV}\mathring{A}$
4. Has a constant value of $-10.2\text{eV}\mathring{A}$

Q.

According to Bohr model of hydrogen, energy is proportional to:-

1. $\frac{-Z^2}{n}$

2. $\frac{-n}{Z^2}$

3. $\frac{-Z^2}{n^2}$

4. $\frac{-n^2}{Z}$

Q. Find the maximum wavelength of electromagnetic radiation which can create an electron - hole pair in silicon whose band gap energy is 1.1 $eV$.

1. 560 $nm$
2. 1130 $nm$
3. 1240 $nm$
4. 870 $nm$

Q. An electron hole pair is formed when light of maximum wavelength $6000\dot{\text{A}}$ is incident on the semiconductor. The band gap energy of the semiconductor is $1.65k\times {10}^{-19}\text{J}$. The value of $k$ .(Integer only) $h=6.62\times {10}^{-34}\text{Js}$

Q. Find the maximum wavelength of electromagnetic radiation which can create a hole - electron pair in germanium. The band gap in germanium is $0.65\text{eV}$.
$(hc=1242\text{eV nm})$

1. $1.9\times {10}^{-6}\text{m}$
2. $2.5\times {10}^{-4}\text{m}$
3. $1.9\times {10}^{-4}\text{m}$
4. $2.5\times {10}^{-6}\text{m}$

Q. Considering Bohr's atomic model to be true if the atomic number is doubled then which of the options are correct.

1. Energy is doubled
2. Radius is doubled
3. Velocity is doubled
4. Radius is halved

Q. An electric in the first orbit of hydrogen atom, has a binding energy of $13.6\text{eV}$. If an electron in another hydrogen atom is in the $n=3$ state, how much energy is required to ionize it?

1. $13.6\text{eV}$
2. $4.53\text{eV}$
3. $3.4\text{eV}$
4. $1.51\text{eV}$

Q.

What is the energy of a hydrogen atom in the first excited state if the potential energy is taken to be zero on the ground state?

Q. The threshold wavelength for photoelectric emission from a material is $5200A^0$.Photoelectrons will be emitted when this material is illuminated with monochromatic radiation from a

1. $50$ watt infrared lamp
2. $1$ watt infrared lamp
3. $50$ watt ultraviolet lamp
4. $1$ watt ultraviolet lamp

Q.

Suppose the energy liberated in the recombination of a hole-electron pair is converted into electromagnetic radiation. If the maximum wavelength emitted is 820 nm, what is the band gap ?

Q. Find the maximum wavelength of electromagnetic radiation which can create an electron - hole pair in silicon whose band gap energy is 1.1 $eV$.

1. 560 $nm$
2. 1130 $nm$
3. 1240 $nm$
4. 870 $nm$

Q.

For Bohr’s atomic model of hydrogen and hydrogen like atoms, answer the following questions based on the columns below. Symbols have their usual meanings and, ‘n’ is principal quantum number, z is atomic number of atom.

$\begin{array}{cccccc}& Column1& & Column2& & Column3\\ & \left(Physicalquanties\right)& & \left(Forhydrogen\right)& & \left(Forhydrogenlikeatom\right)\\ \left(I\right)& Energyof{e}^{-}\left(E\right)is& \left(i\right)& n^3& \left(P\right)& \frac{z^2}{n^2}\\ & proportionalto& & & & \\ \left(II\right)& Velocityof{e}^{-}is& \left(ii\right)& n& \left(Q\right)& \frac{n}{z}\\ & proportionalto& & & & \\ \left(III\right)& Timeperiodofrevolution& \left(iii\right)& \frac{1}{n^2}& \left(R\right)& n\\ & proportionalto& & & & \\ \left(IV\right)& Angularmomentumis& \left(iv\right)& \frac{1}{n}& \left(s\right)& \frac{n^3}{z^2}\\ & proportionalto& & & & \end{array}$

Which option correctly matches with velocity of electron?

1. (II), (iii), (S)

2. (II), (i), (S)

3. (II), (iv), (Q)

Q. A $p$-type semiconductor has acceptor level $57\text{meV}$ above the valence band. Find the maximum wavelength of light which can create a hole.

1. $4.36\times {10}^{-3}\text{m}$
2. $4.36\times {10}^{-5}\text{m}$
3. $2.18\times {10}^{-3}\text{m}$
4. $2.18\times {10}^{-5}\text{m}$

Q. According to Bohr's theory, the energy of an electron in the $n^{th}$ orbit of an atom of atomic number Z is proportional to

1. $\frac{Z^2}{n^2}$
2. $\frac{Z^2}{n}$
3. $\frac{Z}{n}$
4. $Z^2{n}^2$

Q. When a certain photosensistive surface is illuminated with monochromatic light of frequency v, the stopping potential for the photo current is-$V_0/2.$ When the surface frequency v/2, the stopping potential is -$V_0.$ The threshold frequency for photoelectric emission is

1. $\frac{5v}{3}$
2. $2v$
3. $\frac{4}{3}v$
4. $\frac{3v}{2}$

Q. In a non isolated atom each orbital is splitted into different sub levels.

1. False
2. True

Q. Find the maximum wavelength of electromagnetic radiation which can create an electron - hole pair in silicon whose band gap energy is 1.1 $eV$.

1. 560 $nm$
2. 1130 $nm$
3. 1240 $nm$
4. 870 $nm$

Q. An electron (charge e) is accelerates from rest in a region of electric field intensity $E$ for time $t$ seconds The De Broglie wavelength of the electron is (h-plank's const.)

Q.

For Bohr’s atomic model of hydrogen and hydrogen like atoms, answer the following questions based on the columns below. Symbols have their usual meanings and, ‘n’ is principal quantum number, z is atomic number of atom.

$\begin{array}{cccccc}& Column1& & Column2& & Column3\\ & \left(Physicalquanties\right)& & \left(Forhydrogen\right)& & \left(Forhydrogenlikeatom\right)\\ \left(I\right)& Energyof{e}^{-}\left(E\right)is& \left(i\right)& n^3& \left(P\right)& \frac{z^2}{n^2}\\ & proportionalto& & & & \\ \left(II\right)& Velocityof{e}^{-}is& \left(ii\right)& n& \left(Q\right)& \frac{n}{z}\\ & proportionalto& & & & \\ \left(III\right)& Timeperiodofrevolution& \left(iii\right)& \frac{1}{n^2}& \left(R\right)& n\\ & proportionalto& & & & \\ \left(IV\right)& Angularmomentumis& \left(iv\right)& \frac{1}{n}& \left(s\right)& \frac{n^3}{z^2}\\ & proportionalto& & & & \end{array}$

Which of the combination correctly matches with the time period of revolution of electron?

1. (III), (iv), (Q)

2. (III), (i), (S)

3. (III), (iii), (P)

4. (IV), (ii), (Q)

Q. For some energy find the ratio of $\lambda photon$ and ${\lambda }_{\text{electron}}$ (Here m is mass of electron)

1. $c\sqrt{\frac{2m}{E}}$
2. $\frac{1}{c}\sqrt{\frac{2m}{E}}$
3. $\frac{1}{c^2}\sqrt{\frac{2m}{E}}$
4. $\frac{1}{c}\sqrt{\frac{2m}{E^2}}$

Q. In a non isolated atom each orbital is splitted into different sub levels.

1. False
2. True

Q. According to Bohr's theory of the hydrogen atom, the total energy of the hydrogen atom with its electron revolving in the $n^{th}$ stationary orbit is proportional to

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

Q.

Arrange the following sets of orbits and species in the increasing order of the energies.

(A) H atom, n=2
(B) He⁺ ion, n=2
(C) Li⁺² ion, n=2
(D) Be⁺³ ion, n=2

1. ADCB

2. DCBA

3. ABCD

4. DBAC

Q. In Bohr's atomic model of hydrogen, let $K,P$ and $E$ are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level:

1. $K$ decreases, $P$ and $E$ increase
2. $P$ decreases, $K$ and $E$ increase
3. $K$ increases, $P$ and $E$ decrease
4. All $K,P$ and $E$ increase

Q. Compare the velocities of electron in
1. H 1st orbit
2. $H{e}^{+}$ 1st orbit
3. $L{i}^{++}$ 2nd orbit

1. (1) > (2) > (3)
2. (1) = (3) > (2)
3. (1) < (3) < (2)
4. None of these