Bohrs Derivations

Q.

Calculate the wavelength of $1\mathrm{st}$ and $2\mathrm{nd}$ line in the Paschen series.

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. The radii of two of the first four Bohr's orbits of the hydrogen atom are in the ratio 1 : 4. The energy difference between them may be:

1. Either 12.09 eV or 10.2 eV
2. Either 2.55 eV or 10.2 eV
3. Either 13.6 eV or 3.4 eV
4. Either 3.4 eV or 0.85 eV

Q. The value of the energy for the first excited state of hydrogen atom is .

1. $-13.6eV$
2. $-3.40eV$
3. $-0.85eV$

Q.

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

1. 486 nm

2. 911.7 $\mathring{A}$

3. 656.5 nm

4. 434 nm

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. Which of the following is the energy of a possible excited state of hydrogen?

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

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. $\frac{4}{9}{r}_2$

2. $4r_2$

3. $\frac{9}{4}{r}_2$

4. $9r_2$

Q.

Which of the following are true according to the postulates of Bohr's theory?

1. When an atom gets the required energy from outside, it jumps from lower orbits to higher orbits and remains there forever.
2. When an atom gets the required energy from outside, it jumps from the lower orbit to a higher orbit and remains there for very short intervals of time and returns back to a lower orbit, radiating energy.
3. Angular momentum of an electron is proportional to $n$.
4. Angular momentum of an electron is independent of $n$.

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. The number of electrons with same spin with n+l =5 are:

1. 6
2. 9
3. 12
4. 18

Q. An electron in an atom jumps in such a way that its kinetic energy changes from $x$ to $\frac{x}{4}$. The change in potential energy will be:

1. $+\frac{3}{2}x$
2. $-\frac{3}{8}x$
3. $+\frac{3}{4}x$
4. $-\frac{3}{4}x$

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

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.

In the following questions two Statement - 1 (Assertion) and Statement - 2 (Reason) are provided. Each question has 4 choices (a), (b), (c) and (d) for its answer, out of which ONLY ONE is correct. Mark your responses from the following options:

Statement - 1 : Electromagnetic radiation will be emitted for the transition $2P_z\to 2p_x$.

Statement - 2 : No transition of electron takes place between $2P_z$ and $2P_x$ orbitals.

1. Both Statement-1 and Statement - 2 are true and Statement - 2 is the correct explanation of Statement - 1

2. Both Statement - 1 and Statement - 2 are true and Statement - 2 is not the correct explanation of Statement - 1

3. Statement - 1 is true but Statement - 2 is false.

4. Statement - 1 is false but Statement - 2 is true.

Q. The value of the energy for the first excited state of hydrogen atom is .

1. $-13.6eV$
2. $-3.40eV$
3. $-0.85eV$

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. $2.19\times {10}^{6}m/s$

2. $4.19\times {10}^{6}m/s$

3. $3.57\times {10}^{6}m/s$

4. $6.00\times {10}^{6}m/s$

Q.

The angular momentum of electron in ‘d‘ orbital is equal to :

1. $0\hslash$

2. $\sqrt{6}\hslash$

3. $\sqrt{2}\hslash$

4. $2\sqrt{3}\hslash$

Q. Which orbit of the triply ionized beryllium $\left(B{e}^{3+}\right)$ has the same orbit radius as that of the ground state of hydrogen atom?

1. $n=2$
2. $n=3$
3. $n=1$
4. $n=4$

Q. The species which has $5^{th}$ ionisation potential equal to 340 eV is:

1. $B^{+}$
2. $C^{+}$
3. $B$
4. $C$

Q. What electronic transition in the $H{e}^{+}$ spectrum would have the same wavelength as the first Lymen transition of hydrogen:-

1. n = 4 to n = 2
2. n = 1 to n = 4
3. n = 4 to n = 3
4. n = 3 to n = 4

Q. The value of the energy for the first excited state of hydrogen atom will be

1. $-13.6eV$
2. $-3.40eV$
3. $-1.51eV$
4. $-0.85eV$

Q. The angular velocity of an electron occupying the second Bohr orbit of $H{e}^{+}$ ion is: (in $s^{-1}$)

1. $2.06\times {10}^{16}$
2. $3.06\times {10}^{16}$
3. $1.06\times {10}^{18}$
4. $2.06\times {10}^{17}$

Q.

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

1. 486 nm

2. 911.7 $\mathring{A}$

3. 656.5 nm

4. 434 nm

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. $\frac{4}{9}{r}_2$

2. $4r_2$

3. $\frac{9}{4}{r}_2$

4. $9r_2$

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 wave length of first member of Balmer series of a hydrogen atom is nearly (The value of Rydberg constant is $1.08\times {10}^7{m}^{-1})$

1. $4400A^0$

2. $5500A^0$

3. $6600A^0$

4. $7700A^0$

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.

The number of waves in the fourth Bohr orbit of hydrogen is

1. 3

2. 4

3. 9

4. 12

Q. The wavenumber for the shortest wavelength transition in the Balmer series of atomic hydrogen is:

1. $2.725\times {10}^6{m}^{-1}$
   
   
2. $2.725\times {10}^{-6}{m}^{-1}$
3. $3.725\times {10}^6{m}^{-1}$
4. $2.725\times {10}^{6}c{m}^{-1}$