Which of the following statements regarding the $H$ atom spectrum is correct?

  • A
    For the limiting line of the Lyman series,$n_1 = 1$ and $n_2 = 10$.
  • B
    The wavelength for the second line of the Balmer series is $\lambda = \frac{16}{3R}$.
  • C
    The maximum frequency for the Paschen series is $v = \frac{R C}{9}$.
  • D
    For the first line of the Brackett series,$n_1 = 5$ and $n_2 = 6$.

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$(i)$ What is the energy of an electron for hydrogen in $J \ atom^{-1}$ and $J \ mol^{-1}$?
$(ii)$ Calculate the energy of this electron per mole for the first transition ($n=1$ to $n=2$).
$(iii)$ Calculate the ionization energy of hydrogen.

Which one of the following is considered as the main postulate of Bohr’s model of atom?

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The electron energy in a hydrogen atom is given by $E_n = (-2.18 \times 10^{-18})/n^2 \ J$. Calculate the energy required to remove an electron completely from the $n = 2$ orbit. What is the longest wavelength of light in $cm$ that can be used to cause this transition?

In Bohr's atomic model,the radius $(r)$ and energy $(E)$ of an orbit $(n)$ are related as:

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