Among the following,the correct statement$(s)$ for electrons in an atom is(are):
$A$. Uncertainty principle rules out the existence of definite paths for electrons.
$B$. 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.
$C$. 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.
$D$. According to Bohr's model,the magnitude of velocity of electrons increases with increase in values of $n$.

  • A
    $A, B, C$
  • B
    $A, B, D$
  • C
    $A, B$
  • D
    $A, C$

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Match the following items:
$A$. Energy of ground state of $He^+$$i$. $+6.04 \text{ eV}$
$B$. Potential energy of $I$ orbit of $H$ atom$ii$. $-27.2 \text{ eV}$
$C$. Kinetic energy of $II$ excited state of $He^+$$iii$. $8.72 \times 10^{-18} \text{ J}$
$D$. Ionization potential of $He^+$$iv$. $-54.4 \text{ eV}$

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Consider the following:
$I$. The electron spin quantum number describes the orientation of the spin of the nucleus with respect to the magnetic field.
$II$. The orbitals represented by the quantum numbers $n=3, l=2, m=+2$ and $n=3, l=2, m=-2$ have the same energy.
$III$. The energy of a photon is directly proportional to wavelength but inversely proportional to wave number.
$IV$. Lyman series of lines appear in ultra-violet region.
The correct statements are:

Which of the following statement$(s)$ is (are) correct?

Match the equations given in List-$I$ with their names in List-$II$.
List-$I$ List-$II$
$(1)$ $\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$ $(A)$ De Broglie equation
$(2)$ $mvr \ge \frac{nh}{2\pi}$ $(B)$ Uncertainty principle
$(3)$ $\lambda = \frac{h}{\sqrt{2m(KE)}}$ $(C)$ Frequency equation of $H$-spectrum
$(4)$ $\nu = 3.29 \times 10^{15} \left( \frac{1}{n_i^2} - \frac{1}{n_f^2} \right)$ $(D)$ Angular momentum is quantized

If the wavelength for an electron emitted from $H$ atom is $3.3 \times 10^{-10} \ m$,then energy absorbed by the electron in its ground state compared to minimum energy required for its escape from the atom,is $.......$ times. (Nearest integer).
[Given $: h = 6.626 \times 10^{-34} \ Js$,Mass of electron $= 9.1 \times 10^{-31} \ kg$ ]

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