If r is the radius of first orbit, the radius of nth orbit of the H atom will be (C.B.S.E. 1989)
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The energy of hydrogen atom in its ground state is -13·6 eV. The energy of the level corresponding to the quantum number n= 5 is
The energy of the hydrogen atom in its ground state (n=1) is -13.6 eV. The energy of the level corresponding to the quantum number n is given by E = (-13.6 eV)/n^2. For n=5, the energy will be (-13.6 eV)/5^2 = 0.54 eV.
At $200 ^\circ C hydrogen molecules have velocity 105 cm sec^{-1} $ . The de-Broglie wavelength in this case is approximately
In a set of degenerate orbitals the electrons distribute themselves to retain similar spins as far as possible. This statement is attributed to
Hund's rule states that for degenerate orbitals (orbitals with the same energy), the electrons occupy the orbitals in such a way that their spins are parallel, maximizing the total spin multiplicity. This rule is based on the principle of maximum multiplicity, which leads to greater stability.
If uncertainty in the position of electron is zero, the uncertainty in its momentum would be
According to the Heisenberg Uncertainty Principle, the position and momentum of a particle cannot be measured with absolute precision simultaneously. If the uncertainty in the position of an electron is zero, it implies that its position is known exactly, leading to an infinite uncertainty in its momentum.
The radius of second Bohr’s orbit is
For which of the following sets of quantum -numbers an electron will have the highest energy ?
The uncertainty in the position of an electron $ (mass 9.1 \times 10^{–28} g) $ moving with a velocity of $ 3.0 \times10^4 cms^{–1} $ accurate up to 0.011% will be
The uncertainty in the position of a particle is given by the Heisenberg Uncertainty Principle: Δx * Δp ≥ h/4π, where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is Planck's constant. Using the given values and the relation p = mv, the uncertainty in position is calculated to be 0.175 cm.
The radius of hydrogen atom in the ground state is $ 0·53 A ^ \circ , the radius of 3_Li ^{2+} $ in the similar state is
The radius of a hydrogen-like atom is inversely proportional to the nuclear charge (Z). For the Li2+ ion, Z = 3. Since the radius of the hydrogen atom is given as 0.53 Ã…, the radius of Li2+ in the ground state will be 0.53/3 = 0.17 Ã….
Splitting of spectral lines under the influence of magnetic field is called
The splitting of spectral lines due to the influence of a magnetic field is known as the Zeeman effect. It is caused by the interaction between the magnetic dipole moment of the electron and the applied magnetic field.
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