Bohr model, energy levels and the hydrogen spectrum — practice questions

Question 1 · difficulty L1 · recall

Bohr postulated that electrons in allowed stationary orbits

• A. radiate continuously and spiral inward
• B. have arbitrary angular momentum
• C. do not radiate energy
• D. must be at rest

Question 2 · difficulty L1 · understanding

Bohr's angular-momentum quantisation is

• A. mvr=nh
• B. mvr=n/h
• C. mv/r=nħ
• D. mvr = nħ

Question 3 · difficulty L2 · understanding

Radius of a certain orbit of hydrogen atom is 8.48 $$\mathop A\limits^o$$. If energy of electron in this orbit is $$E / x$$. then $$x=$$ ________ (Given $$\mathrm{a}_0=0.529$$ $$\mathop A\limits^o$$, $$E=$$ energy of electron in ground state).

Question 4 · difficulty L2 · understanding

The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is $$915\mathop A\limits^o$$. The longest wavelength of spectral lines in the Balmer series will be _______ $$\mathop A\limits^o$$.

Question 5 · difficulty L2 · understanding

If Rydberg's constant is $$R$$, the longest wavelength of radiation in Paschen series will be $$\frac{\alpha}{7 R}$$, where $$\alpha=$$ ________.

Question 6 · difficulty L2 · understanding

The radius of $$2^{\text {nd }}$$ orbit of $$\mathrm{He}^{+}$$ of Bohr's model is $$r_{1}$$ and that of fourth orbit of $$\mathrm{Be}^{3+}$$ is represented as $$r_{2}$$. Now the ratio $$\frac{r_{2}}{r_{1}}$$ is $$x: 1$$. The value of $$x$$ is ___________.

Question 7 · difficulty L2 · understanding

The radius of fifth orbit of the $$\mathrm{Li}^{++}$$ is __________ $$\times 10^{-12} \mathrm{~m}$$. Take: radius of hydrogen atom $$= 0.51\,\mathop A\limits^o$$

Question 8 · difficulty L2 · understanding

If the binding energy of ground state electron in a hydrogen atom is $13.6\, \mathrm{eV}$, then, the energy required to remove the electron from the second excited state of $\mathrm{Li}^{2+}$ will be : $x \times 10^{-1} \mathrm{eV}$. The value of $x$ is ________.

Question 9 · difficulty L2 · understanding

For hydrogen atom, $$\lambda_{1}$$ and $$\lambda_{2}$$ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of $$\lambda_{1}$$ and $$\lambda_{2}$$ is $$\frac{x}{32}$$. The value of $$x$$ is __________.

Question 10 · difficulty L2 · understanding

$${x \over {x + 4}}$$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) third permitted energy level to the second level and (ii) the highest permitted energy level to the second permitted level. The value of x will be ____________.