A dye absorbs a photon of wavelength $\mathrm{\lambda }$ and re-emits the same energy into two photons of wavelengths ${\mathrm{\lambda }}_1$ and ${\mathrm{\lambda }}_2$ respectively. The wavelength $\mathrm{\lambda }$ is related to ${\mathrm{\lambda }}_1$ and ${\mathrm{\lambda }}_2$ as-

1.  $\mathrm{\lambda }=\frac{{\mathrm{\lambda }}_1+{\mathrm{\lambda }}_2}{{\mathrm{\lambda }}_1{\mathrm{\lambda }}_2}$

2.  $\mathrm{\lambda }=\frac{{\mathrm{\lambda }}_1{\mathrm{\lambda }}_2}{{\mathrm{\lambda }}_1+{\mathrm{\lambda }}_2}$

3.  $\mathrm{\lambda }=\frac{{\mathrm{\lambda }}_1^2+{\mathrm{\lambda }}_2^2}{{\mathrm{\lambda }}_1+{\mathrm{\lambda }}_2}$

4.  $\mathrm{\lambda }=\frac{{\mathrm{\lambda }}_1{\mathrm{\lambda }}_2}{{\left({\mathrm{\lambda }}_1+{\mathrm{\lambda }}_2\right)}^2}$

The energy of an electron in the first Bohr's orbit of an H-atom is -13.6 eV. The possible energy value (s) of the excited state(s) for electrons in Bohr's orbits of hydrogen is (are):

1. -3.4 eV

2. -4.2 eV

3. -6.8 eV

4. +6.8 eV

Assertion: The angular momentum of an electron in an atom is quantized.

Reason: In an atom only those orbits are permitted in which angular momentum of the electron is a natural number multiple of $\frac{h}{2\mathrm{\pi }}$.

1. Both the assertion and the reason are true and the reason is the correct explanation of the assertion. 

2. Both the assertion and the reason are true but the reason is not the correct explanation of the assertion.

3. The assertion is true but the reason is false.

4. The assertion is false but the reason is true.

For any H like system, the ratio of velocities of I, II & III orbit i.e., ${\mathrm{V}}_1 : {\mathrm{V}}_2 : {\mathrm{V}}_3$ will be

1.  1 : 2 : 3

2.  1 : 1/2 : 1/3

3.  3 : 2 : 1

4.  1 : 1 : 1

The concept that contradicts the Bohr Model of an atom is 

1. Rutherford Model

2. Heisenberg's Uncertainty Principle

3. J.J. Thomson Model

4. Photoelectric Effect

An ion among the following that has the same radius as a hydrogen atom, having n=1, is 

1. ${\mathrm{He}}^{+}, n=2$

2. ${\mathrm{Li}}^{2+},n=2$

3. ${\mathrm{Be}}^{3+}, n=2$

4. ${\mathrm{Li}}^{2+},\mathrm{n}=3$

Assertion: Bohr’s orbits are also called stationary states.

Reason:  Electrons are stationary in an orbit.

1. Both the assertion and the reason are true and the reason is the correct explanation of the assertion.

2. Both the assertion and the reason are true but the reason is not the correct explanation of the assertion.

3. The assertion is true but the reason is false.

4. The assertion is false but the reason is true.

Assertion: The radius of the second orbit of He⁺ is equal to that of the first orbit of hydrogen.

Reason: The radius of an orbit in hydrogen-like species is directly proportional to n and inversely proportional to Z.

1. Both the assertion and the reason are true and the reason is the correct explanation of the assertion.

2. Both the assertion and the reason are true but the reason is not the correct explanation of the assertion.

3. The assertion is true but the reason is false.

4. Both assertion and reason are false statements.

If the size of the first orbit of the hydrogen atom is 5.29 nm, the size of the second orbit of He⁺ is

1. 2.65 nm

2. 21.16 nm

3. 10.58 nm

4. 5.29 nm

The wavelength of a certain line in the Balmer series is observed to 4341 A^o for hydrogen atoms. The electronic transition may be

$$\begin{gathered} 1. 3 \to 2 \\ 2. 4 \to 1 \\ 3. 5 \to 2 \\ 4. 5 \to 3 \end{gathered}$$