The energy levels for a hydrogen-like species with atomic number $Z$ can be given by:

  • A
    $E_n$ for species $= Z^2 \times E_n$ for $H$
  • B
    $E_n$ for species $= Z \times E_n$ for $H$
  • C
    $E_n$ for species $= \frac{1}{Z^2} \times E_n$ for $H$
  • D
    $E_n$ for species $= \frac{1}{Z} \times E_n$ for $H$

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The radii of two of the first four Bohr’s orbits of the hydrogen atom are in the ratio $1 : 4$. The energy difference between them may be

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$E_{n} = \text{Total energy}, K_{n} = \text{Kinetic energy}, V_{n} = \text{Potential energy}, r_{n} = \text{Radius of } n^{\text{th}} \text{ orbit}$
Match the following:
Column $I$ Column $II$
$A$. $V_{n} / K_{n} = ?$ $P$. $0$
$B$. If radius of $n^{\text{th}}$ orbit $\propto E_{n}^{x}, x = ?$ $Q$. $-1$
$C$. Angular momentum in lowest orbital $R$. $-2$
$D$. $1/r_{n} \propto Z^{y}, y = ?$ $S$. $1$

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The quantity $h \nu / K_{B}$ corresponds to

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