Bohrs Derivations

Q.

The Bohr orbit radius for the hydrogen atom ( n= 1) is approximately 0.530 $A^{\circ }$. The radius for the first excited state (n=2) orbit is:

1. 4.77A^∘

2. 2.12A^∘

3. 1.06A^∘

4. 0.13 A^∘

Q. The KE and PE (in eV) of electron present in third Bohr’s orbit of hydrogen atom respectively are

1. –1.51, –3.02
2. 1.51, –3.02
3. –3.02, 1.51
4. 1.51, –1.51

Q.

What is the wavelength of the light emitted when an electron in a hydrogen atom undergoes transition from the energy level n = 4 to energy level n = 2? What is the colour corresponding to their wavelengths? (Given $R_H=109677c{m}^{-1}$)

1. 486 nm, Blue

2. 576 nm, Blue

3. 450 nm, Blue

4. 650, Blue

Q.

The circumference of the first Bohr orbit in H atom is $3.322\times {10}^{-10}m$. What is the velocity of the electron of this orbit?

1. 2.19 × 10⁶ m/s

2. 4.19 × 10⁶ m/s

3. 3.57 × 10⁶ m/s

4. 6.00 × 10⁶ m/s

Q.

Why is Gold unreactive?

Q.

The electron belongs to the angular momentum of an $e^{-}$in a Bohr's orbit of H atom is $4.2178\times {10}^{-34}Kg.m^2.Se{c}^{-1}$.

1. M - shell

2. K - shell

3. L - shell

4. N - shell

Q.

A spectral line in the spectrum of H atom has a wavenumber of $15222.22c{m}^{-1}$ . The transition responsible for this radiation is (Rydberg constant $R=109677c{m}^{-1}$)

1. 

2. 

3. 

4. 

Q.

If the radius of the second Bohr orbit of hydrogen atom is $r_2$, the radius of the third Bohr orbit will be

1. 

2. 

3. 

4. 

Q. The energy of an electron present in Bohr’s second orbit of hydrogen atom is

1. 
2. 
3. 
4. 

Q.

Calculate the wavelength of the first time in the Balmer series of hydrogen spectrum.

1. 656.5 nm

2. 486 nm

3. 911.7

4. 434 nm

Q. Ratio of radius of first orbit of $H{e}^{+}$ to the second orbit of hydrogen atom will be

1. $1:1$
2. $1:2$
3. $1:8$
4. $1:4$

Q.

The radius of first Bohr's orbit in H-atoms is $r_1$. The corresponding wavelength of an electron in 2nd orbit is:

1. $6\pi r_1$

2. $4\pi r_1$

3. $2\pi r_1$

4. $3\pi r_1$

Q. The energy of an electron present in Bohr’s second orbit of hydrogen atom is

1. $-1312Jato{m}^{-1}$
2. $-328kJmo{l}^{-1}$
3. $-328Jmo{l}^{-1}$
4. $-164kJmo{l}^{-1}$

Q.

Calculate the energy associated with the first orbit of $H{e}^{\oplus }$. What is the radius of orbit?

1. 0.3026 nm
2. 0.20645 nm
3. 0.02645 nm
4. 0.03026 nm

Q. If the first excitation energy for an H-like (hypothetical) sample is 24 eV, then the separation energy of an electron in the 3rd excited state is:

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

Q.

The Bohr orbit radius for the hydrogen atom (n=1) is approximately $0.530\dot{A}$. The radius for the first excited state (n=2)

1. 

2. 

3. 

4. 

Q.

The radius of the second Bohr orbit for hydrogen atom is:
(Plank’s const. H = 6.6262 x${10}^{-34}$Js; mass of electron = 9.1091 x ${10}^{-31}$kg; charge of electron e = 1.60210 x ${10}^{-19}$C; permittivity of vaccum ${ϵ}_0=8.854185\times {10}^{-12}k{g}^{-1}{m}^{-3}{A}^2)$

1. 1.65Å
2. 4.76Å
3. 0.529Å
4. 212Å

Q.

What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition n = 4 to n = 2 in the $H{e}^{\oplus }$ spectrum?

1. n = 4 to n = 2

2. n = 3 to n = 1

3. n = 3 to n = 2

4. n = 2 to n = 1

Q.

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [$a_0$ is Bohr radius]

1. 

2. 

3. 

4. 

Q. Orbital angular momentum of electron in $3d$orbital is

1. $\sqrt{3}\hslash$
2. $\sqrt{2}\hslash$
3. $\sqrt{6}\hslash$
4. $\sqrt{8}\hslash$

Q.

What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition n = 4 to n = 2 in the $H{e}^{\oplus }$ spectrum?

1. n = 4 to n = 2

2. n = 3 to n = 2

3. n = 3 to n = 1

4. n = 2 to n = 1

Q.

Which of the following is true for Bohr's model?

1. An electron can move only in those orbits for which its angular momentum is an integral multiple of

2. Electrons revolve around nucleus in discrete and quantized energy levels/orbits.

3. The energy of an electron in the orbit do not change with time.

4. Electron will move from a lower stationary state to a higher stationary state when required amount of energy is absorbed.

Q.

The transition from state n = 4 to n = 3 in a $H{e}^{+}$ ion result in ultraviolet radiation. Infrared radiation will be obtained in the transition from

1. $n=2\to n=1$

2. $n=3\to n=2$

3. $n=5\to n=4$

4. $n=8\to n=6$

Q. If the value of $E_n=-78.4kcalmo{l}^{-1}$, the order of the orbit in hydrogen atom is:

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

Q. What is the ratio of time periods $\left(T_1/T_2\right)$ in the second orbit of hydrogen atom to the third orbit of an $H{e}^{+}$ ion?

1. 8/27
2. 32/27
3. 27/32
4. None of these

Q. The angular momentum of electron in 'd' orbital is equal to:

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Q. If the radius of $3^{rd}$ Bohr’s orbit of H-atom is r, then the radius of $4^{th}$ Bohr’s orbit of $H{e}^{+}$ would be

1. $r\times \frac{4}{3}$
2. $r\times \frac{16}{9}$
3. $r\times \frac{8}{9}$
4. $r\times \frac{9}{8}$

Q.

The electron belongs to the angular momentum of an $e^{-}$in a Bohr's orbit of H atom is $4.2178\times {10}^{-34}Kg.m^2.Se{c}^{-1}$.

1. K - shell

2. L - shell

3. N - shell

4. M - shell

Q. For a hypothetical hydrogen like atom, the potential energy of the system is given by $U_{\left(r\right)}\left(r\right)=\frac{-K{e}^2}{r^3}$, where $r$ is the distance between the two particles. If Bohr’s model of quantization of angular momentum is applicable, then the velocity of the particle is given by:

1. $v=\frac{n^2{h}^3}{K{e}^{2}8{\pi }^3{m}^2}$
2. $v=\frac{n^3{h}^3}{8K{e}^2{\pi }^2{m}^2}$
3. $v=\frac{n^3{h}^3}{24K{e}^2{\pi }^3{m}^2}$
4. $v=\frac{n^3{h}^3}{24K{e}^2{\pi }^3{m}^3}$

Q.

What is the maximum number of emission lines when the excited electron of a H atom in n = 6 drops to the ground state?

1. 21

2. 15

3. 6

4. 10