For the Paschen series, the values of $n_1$ and $n_2$ in the expression $\Delta E = R h c \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$ are:

  • A
    $n_1 = 1, n_2 = 2, 3, 4 \dots$
  • B
    $n_1 = 2, n_2 = 3, 4, 5 \dots$
  • C
    $n_1 = 3, n_2 = 4, 5, 6 \dots$
  • D
    $n_1 = 4, n_2 = 5, 6, 7 \dots$

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What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition $n=4$ to $n=2$ of $He^{+}$ spectrum?

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According to Bohr's atomic theory :-
$A$. Kinetic energy of electron is $\propto \frac{Z^{2}}{n^{2}}$.
$B$. The product of velocity $(v)$ of electron and principal quantum number $(n)$,'$vn$' $\propto Z^{2}$.
$C$. Frequency of revolution of electron in an orbit is $\propto \frac{Z^{3}}{n^{3}}$.
$D$. Coulombic force of attraction on the electron is $\propto \frac{Z^{3}}{n^{4}}$.
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