Atomic Structure · JEE Advanced previous year questions

Regarding the molecular orbital (MO) energy levels for homonuclear diatomic molecules, the $\text{INCORRECT}$ statement(s) is(are)

1. A.Bond order of $\mathrm{N}{\mathrm{e}}_2$ is zero.
2. B.The highest occupied molecular orbital (HOMO) of ${\mathrm{F}}_2$ is $\sigma$-type.
3. C.Bond energy of ${\mathrm{O}}_2^{+}$ is smaller than the bond energy of ${\mathrm{O}}_2$.
4. D.Bond length of $\mathrm{L}{\mathrm{i}}_2$ is larger than the bond length of ${\mathrm{B}}_2$.

Among the following, the correct statement(s) for electrons in an atom is(are)

1. A.Uncertainty principle rules out the existence of definite paths for electrons.
2. B.The energy of an electron in $2s$ orbital of an atom is lower than the energy of an electron that is infinitely far away from the nucleus.
3. C.According to Bohr’s model, the most negative energy value for an electron is given by n = 1, which corresponds to the most stable orbit.
4. D.According to Bohr’s model, the magnitude of velocity of electrons increases with increase in values of n.

According to Bohr’s model, the highest kinetic energy is associated with the electron in the

1. A.first orbit of H atom
2. B.first orbit of $\mathrm{H}{\mathrm{e}}^{+}$
3. C.second orbit of $\mathrm{H}{\mathrm{e}}^{+}$
4. D.second orbit of $\mathrm{L}{\mathrm{i}}^{2+}$

1. A.$1\sigma <1{\sigma }^{\ast }<1\pi <2\sigma <1{\pi }^{\ast }<2{\sigma }^{\ast }$
2. B.$1\sigma <1{\sigma }^{\ast }<1\pi <2\sigma <2{\sigma }^{\ast }<1{\pi }^{\ast }$
3. C.$1\sigma <1{\sigma }^{\ast }<2\sigma <1\pi <1{\pi }^{\ast }<2{\sigma }^{\ast }$
4. D.$1\sigma <1{\sigma }^{\ast }<2\sigma <1\pi <2{\sigma }^{\ast }<1{\pi }^{\ast }$

For ${\mathrm{He}}^{+}$, a transition takes place from the orbit of radius $105.8\text{ pm}$ to the orbit of radius $26.45\text{ pm}$. The wavelength (in $\text{nm}$) of the emitted photon during the transition is _____. [Use: Bohr radius, $a=52.9\text{ pm}$ Rydberg constant, $R_{\mathrm{H}}=2.2\times 10^{-18}\text{ J}$ Planck's constant, $h=6.6\times 10^{-34}\text{ J s}$ Speed of light, $c=3\times 10^8{\text{ m s}}^{-1}$]