Bohrs Derivations

Q. Not considering the electronic spin, the degeneracy of the second excited state (n = 3) of H atom is 9, while the degeneracy of the second excited state of $H^{-}$ is:___

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.

Calculate the radius of the third orbit of a hydrogen atom; the radius of the first Bohr orbit of hydrogen atom is 0.53 Å.

1. 4.77 Å

2. 1.59 Å

3. 1.06 Å

4. 2.12 Å

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.

What is the maximum number of emission lines when the excited electron of a hydrogen atom in $\mathrm{n}=6$ drops to the ground state?

1. $10\mathrm{lines}$

2. $12\mathrm{lines}$

3. $15\mathrm{lines}$

4. $18\mathrm{lines}$

Q.

Obtain An Expression For The Radius Of Bohr Orbit.

Q.

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

1. 486 nm

2. 434 nm

3. 911.7 Å

4. 656.5 nm

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

1. 9
2. 3
3. 4

Q. If the radius of the first Bohr orbit of hydrogen atom is 0.53 Å, the radius of the third orbit of a hydrogen atom is .

1. 4.77 Å
2. 1.59 Å
3. 2.12 Å

Q.

According to Bohr atom model, in which of the following transitions will the frequency be maximum?

1. $n=2ton=1$

2. $n=4ton=3$

3. $n=5ton=4$

4. $n=3ton=2$

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. 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. Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following, List-I contains some quantities for the $n^{th}$ orbit of the atom and List-II contains options showing how they depend on n.

$\begin{array}{cccc}& \text{List-I}& & \text{List-II}\\ \text{(I)}& \text{Radius of the}{n}^{th}\text{orbit}& \text{(P)}& \propto n^{-2}\\ \text{(II)}& \text{Angular momentum of the electron in the}{n}^{th}\text{orbit}& \text{(Q)}& \propto n^{-1}\\ \text{(III)}& \text{Kinetic energy of the electron in the}{n}^{th}\text{orbit}& \text{(R)}& \propto n^0\\ \text{(IV)}& \text{Potential energy of the electron in the}{n}^{th}\text{orbit}& \text{(S)}& \infty n^1\\ & & \text{(T)}& \propto n^2\\ & & \text{(U)}& \propto n^{\frac{1}{2}}\end{array}$

Which of the following options has the correct combination considering List-I and List-II ?

1. (III), (P)
2. (IV), (U)
3. (III), (S)
4. (IV), (Q)

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

1. -0.85eV

2. -13.6eV

3. -3.40eV

4. -1.51eV

Q.

A proton of energy $8eV$ is moving in a circular path in a uniform magnetic field. The energy of an alpha particle moving in the same magnetic field and along the same path will be

1. $4eV$

2. $2eV$

3. $8eV$

4. $6eV$

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

Q.

The ratio between radii of $H{e}^{+}$ ion and H atom is

1. $\frac{1}{2}$

2. 1

3. $\frac{3}{2}$

4. 2

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 value of ${\mathrm{n}}_1$ in Balmer theory?

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

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

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 of the following statement(s) is/are correct regarding inter-halogen compounds of ABx types?

1. x may be 1, 3, 5 and 7.

2. A is a more electronegative halogen than B.

3. $FB{r}_3$ cannot exit.

4. The structures of $Cl{F}_3$ and $I{F}_7$ show deviation from normal structures and could be explained on the basis of VSEPR theory.

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°

2. 5500A°

3. 7700A°

4. 6600A°

Q.

What is quantization or quantum no.

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

Q. Not considering the electron spin, the degeneracy of the second excited state $n=3$, of $H$ atom is $9$, while the degeneracy of the second excited state of $H^{-}$ is:

Q.

The ratio between radii of $H{e}^{+}$ ion and H atom is

1. 1

2. 2

3. 1/2

4. 3/2

Q.

Define energy levels.

Q. An electron in the hydrogen atom is de-excited from $5^{th}$ orbit to $1^{st}$ orbit. The number of spectral lines the element is expected to emit:

1. 5
2. 4
3. 10
4. 12

Q.

The ratio of the minimum wavelength of the Lyman and Balmer series will be:

1. $10$

2. $0.5$

3. $0.25$

4. $1.25$