Spectrum of the hydrogen atom — practice questions

Question 1 · difficulty L2 · understanding

Wavenumber for a radiation having 5800 $$\mathop A\limits^o$$ wavelength is $$x \times 10 \mathrm{~cm}^{-1}$$ The value of $$x$$ is ________. (Integer answer)

Question 2 · difficulty L2 · understanding

When the excited electron of a H atom from n = 5 drops to the ground state, the maximum number of emission lines observed are _____________.

Question 3 · difficulty L2 · understanding

If shortest wavelength of hydrogen atom in Lyman series is $x$, then longest wavelength in Balmer series of $\mathrm{He}^{+}$is:

• A. $\frac{9 x}{5}$
• B. $\frac{36 x}{5}$
• C. $\frac{x}{4}$
• D. $\frac{5 x}{9}$

Question 4 · difficulty L2 · understanding

What is the ratio of wave number of first line (lowest energy line) of Balmer series of H atomic spectrum to first line of its Brackett series?

• A. 5 : 1
• B. 5 : 0.81
• C. 5 : 1.75
• D. 5 : 27

Question 5 · difficulty L2 · understanding

Match List I with List II List - I (Spectral Series for Hydrogen) List - II (Spectral Region/Higher Energy State) (A) Lyman (I) Infrared region (B) Balmer (II) UV region (C) Paschen (III) Infrared region (D) Pfund (IV) Visible region Choose the correct answer from the options given below:

• A. A-II, B-IV, C-III, D-I
• B. A-I, B-III, C-II, D-IV
• C. A-II, B-III, C-I, D-IV
• D. A-I, B-II, C-III, D-IV

Question 6 · difficulty L3 · understanding

The hydrogen spectrum consists of several spectral lines in Lyman series $\left(L_1, L_2\right.$, $\mathrm{L}_3 \ldots ; \mathrm{L}_1$ has lowest energy among Lyman series). Similarly it consists of several spectral lines in Balmer series $\left(\mathrm{B}_1, \mathrm{~B}_2, \mathrm{~B}_3 \ldots ; \mathrm{B}_1\right.$ has lowest energy among Balmer lines). The energy of $L_1$ is $x$ times the energy of $B_1$. The value of $x$ is $\_\_\_\_$ $\times 10^{-1}$ . (Nearest integer)

Question 7 · difficulty L3 · understanding

Number of spectral lines obtained in $$\mathrm{He}^{+}$$ spectra, when an electron makes transition from fifth excited state to first excited state will be

Question 8 · difficulty L3 · understanding

If wavelength of the first line of the Paschen series of hydrogen atom is 720 nm, then the wavelength of the second line of this series is _________ nm. (Nearest integer)

Question 9 · difficulty L3 · understanding

$\mathbf{X}^{\boldsymbol{a}+}$ and $\mathbf{Y}^{\boldsymbol{b}+}$ are hydrogen-like species. The wavelength of light absorbed during the transition between the states with principal quantum numbers $n=1$ and $n=2$ of $\mathbf{X}^{\boldsymbol{a}+}$ is $\lambda$. The wavelength of light absorbed during the transition between the states with principal quantum numbers $n=2$ and $n=4$ of $\mathbf{Y}^{\boldsymbol{b}+}$ is $9 \lambda$. The lowest possible value of $(\boldsymbol{a}+\boldsymbol{b})$ is $\_\_\_\_$ .

Question 10 · difficulty L3 · understanding

The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series. ( $\mathrm{R}=$ Rydberg constant)

• A. $\frac{5 \mathrm{R}}{36}, \frac{3 \mathrm{R}}{16}, \frac{21 \mathrm{R}}{100}$
• B. $\frac{7 \mathrm{R}}{144}, \frac{3 \mathrm{R}}{16}, \frac{16 \mathrm{R}}{255}$
• C. $\frac{3 \mathrm{R}}{4}, \frac{3 \mathrm{R}}{16}, \frac{7 \mathrm{R}}{144}$
• D. $\frac{5 \mathrm{R}}{36}, \frac{8 \mathrm{R}}{9}, \frac{15 \mathrm{R}}{16}$