Question
Which one is the wrong statement?
A.
de-Broglie’s wavelength is given by $$\lambda = \frac{h}{{mv}},$$ where $$m=$$ Mass of the particle, $$v=$$ group velocity of the particle
B.
The uncertainty principle is $$\Delta E \times \Delta t \geqslant \frac{h}{{4\pi }}$$
C.
Half-filled and fully filled orbitals have greater stability due to greater exchange energy, greater symmetry and more balanced arrangement
D.
The energy of $$2s$$ - orbital is less than the energy of $$2p$$ - orbital in case of hydrogen like atoms
Answer :
The energy of $$2s$$ - orbital is less than the energy of $$2p$$ - orbital in case of hydrogen like atoms
Solution :
(A) According to de-Broglie’s equation,
$${\text{Wavelength}}\left( \lambda \right) = \frac{h}{{mv}}$$
where, $$h =$$ Planck's constant.
Thus, statement (A) is correct.
(B) According to Heisenberg uncertainty principle,
the uncertainties of position $$\left( {\Delta x} \right)$$ and
momentum $$\left( {p = m\Delta v} \right)$$ are related as
$$\eqalign{
& \Delta x.\,\,\Delta p \geqslant \frac{h}{{4\pi }} \cr
& {\text{or,}}\,\,\Delta x.\,\,m\Delta v \geqslant \frac{h}{{4\pi }} \cr
& \Delta x.\,\,m.\,\,\Delta a.\,\,\Delta t \geqslant \frac{h}{{4\pi }} \cr
& \left[ {\frac{{\Delta v}}{{\Delta t}} = \Delta a,\,\,a = {\text{acceleration }}} \right] \cr
& {\text{or,}}\Delta {\text{x}}\,.\,\,F.\,\,\Delta t \geqslant \frac{h}{{4\pi }}\,\,\left[ {\because \,\,F = m.\,\,\Delta a} \right] \cr
& {\text{or,}}\,\,\Delta {\text{E}}{\text{.}}\,\,\Delta {\text{t}} \geqslant \frac{h}{{4\pi }}\,\,\left[ {\because \Delta E = F.\,\,\Delta x.\,\,E = {\text{energy}}} \right] \cr} $$
Thus, statement (B) is correct.
(C) The half and fully filled orbitals have greater stability due to greater exchange energy,
greater symmetry and more balanced arrangement. Thus statement (C) is correct.
(D) For a single electronic species like $$H,$$ energy depends on value of $$n$$ and does not depend on $$l$$ Hence energy of $$2s$$ - orbital. and $$2p$$ - orbital is equal in case of hydrogen like species. Therefore, statement (D) is incorrect.