Chapter 13

A photon of \(400 \mathrm{~nm}\) is absorbed by a gas molecule and then the molecule re-emits two photons. One re-emitted photon has wavelength \(500 \mathrm{~nm}\). Assuming that there is no change in the energy of molecule, the wavelength of second re-emitted photon is (a) \(100 \mathrm{~nm}\) (b) \(2000 \mathrm{~nm}\) (c) \(-100 \mathrm{~nm}\) (d) \(900 \mathrm{~nm}\)

A green bulb and a red bulb are emitting the radiations with equal power. The correct relation between numbers of photons emitted by the bulbs per second is (a) \(n_{\mathrm{g}}=n_{\mathrm{r}}\) (b) \(n_{\mathrm{g}}n_{\mathrm{r}}\) (d) unpredictable

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is \(\left(a_{\mathrm{o}}\right.\) is the Bohr radius) (a) \(\frac{h^{2}}{4 \pi^{2} m a_{0}^{2}}\) (b) \(\frac{h^{2}}{16 \pi^{2} m a_{o}^{2}}\) (c) \(\frac{h^{2}}{32 \pi^{2} m a_{o}^{2}}\) (d) \(\frac{h^{2}}{64 \pi^{2} m a_{o}^{2}}\)

Wavelength of photon which have energy equal to average of energy of photons with \(\lambda_{1}=4000 \AA\) and \(\lambda_{2}=6000 \AA\) will be (a) \(5000 \AA\) (b) \(4800 \AA\) (c) \(9600 \AA\) (d) \(2400 \AA\)

The ionization energy of a hydrogen-like atom is \(14.4 \mathrm{eV} .\) The amount of energy released when electron jumps from the fourth orbit to the first orbit in this atom, is (a) \(13.5 \mathrm{eV}\) (b) \(10.8 \mathrm{eV}\) (c) \(0.9 \mathrm{eV}\) (d) \(12.75 \mathrm{eV}\)

The radius of first orbit of H-atoms is \(0.529 \AA\). The radius of first orbit of D-atoms should be (a) exactly \(0.529 \AA\) (b) slightly less than \(0.529 \AA\) (c) slightly greater than \(0.529 \AA\) (d) \(1.058 \AA\)

Wavelength of photon having energy \(1 \mathrm{eV}\) would be (a) \(1.24 \times 10^{-4} \mathrm{~m}\) (b) \(1.24 \times 10^{-6} \mathrm{~m}\) (c) \(1.24 \times 10^{-5} \mathrm{~m}\) (d) \(1.24 \times 10^{4} \mathrm{~m}\)

The ionization energy of H-atoms is \(13.6 \mathrm{eV}\). The ionization energy of deuterium atom should be (a) exactly \(13.6 \mathrm{eV}\) (b) slightly less than \(13.6 \mathrm{eV}\) (c) slightly greater than \(13.6 \mathrm{eV}\) (d) \(27.2 \mathrm{eV}\)

In the emission of photoelectrons, the number of photoelectrons emitted per unit time depends upon (a) energy of the incident radiation (b) intensity of the incident radiation (c) frequency of the incident radiation (d) wavelength of the incident radiation

A photo sensitive surface is receiving light of wavelength \(5000 \AA\) at the rate of \(10^{-7} \mathrm{~J} / \mathrm{s}\). The number of photons received per second is (a) \(2.5 \times 10^{11}\) (b) \(3.0 \times 10^{32}\) (c) \(2.5 \times 10^{18}\) (d) \(2.5 \times 10^{9}\)

Sodium atoms emit a spectral line with a wavelength in the yellow, \(589.6 \mathrm{~nm}\). What is the approximate difference in energy between the two energy levels involved in the emission of this spectral line? (a) \(3.37 \times 10^{-19} \mathrm{~J}\) (b) \(2.1 \mathrm{eV}\) (c) \(48.35 \mathrm{kcal} / \mathrm{mol}\) (d) all of these

A certain molecule has an energy level diagram for its vibrational energy in which two levels are \(0.0141 \mathrm{eV}\) apart. The wavelength of the emitted line for the molecule as it falls from one of these levels to the other, is about (a) \(88 \mu \mathrm{m}\) (b) \(88 \mathrm{~mm}\) (c) \(174.84 \mathrm{~m}\) (d) \(88 \mathrm{~nm}\)

In a discharge tube, there are only two hydrogen atoms. If the electrons in both atoms are de-exciting from \(4^{\text {th }}\) orbit, the minimum and maximum number of spectral lines should, respectively, be (a) 1,4 (b) 4,1 (c) 3,4 (d) 1,6

Electrons are de-exciting from the fifth orbit in hydrogen atoms but the first orbit is not available for them. The maximum number of spectral lines should be (a) 10 (b) 6 (c) 15 (d) 3

If the radius of first orbit of \(\mathrm{H}\) -atom is \(x \AA\), then the radius of the second orbit of \(\mathrm{Li}^{2+}\) ion will be (a) \(x \AA\) (b) \(\frac{4 x}{3} \AA\) (c) \(\frac{9 x}{2} \AA\) (d) \(4 x \AA\)

When electron jumps from the fourth orbit to the second orbit in \(\mathrm{He}^{+}\) ion, the radiation emitted out will fall in (a) ultraviolet region (b) visible region (c) infrared region (d) radio wave region

When electrons are de-exciting to the ground state from \(n^{\text {th }}\) orbit of hydrogen atoms, 15 spectral lines are formed. The shortest wavelength among these will be (a) \(\frac{11}{900} R\) (b) \(\frac{900}{11 R}\) (c) \(\frac{35}{36} R\) (d) \(\frac{35}{36 R}\)

What would be the approximate quantum number, \(n\), for a circular orbit of hydrogen, \(1 \times 10^{5} \mathrm{~cm}\) in diameter? (a) 31 (b) 43 (c) 40 (d) 39

The wavelengths of the first Lyman lines of hydrogen, \(\mathrm{He}^{+}\) and \(\mathrm{Li}^{2+}\) ions are \(\lambda_{1}, \lambda_{2}\), \(\lambda_{3} .\) The ratio of these wavelengths is (a) \(1: 4: 9\) (b) \(9: 4: 1\) (c) \(36: 9: 4\) (d) \(6: 3: 2\)

The ratio of circumference of third and second orbits of \(\mathrm{He}^{+}\) ion is (a) \(3: 2\) (b) \(2: 3\) (c) \(9: 4\) (d) \(4: 9\)

The wavelength of first line of Lyman series of \(\mathrm{H}\) -atom is \(1216 \AA\). What will be the wavelength of first line of Lyman series in 10 time ionized sodium atom \((Z=11)\) (a) \(1216 \AA\) (b) \(12.16 \AA\) (c) \(10 \AA\) (d) \(110 \AA\)

Imagine an atom made up of a stationary proton and a hypothetical particle of double the mass of electron but having the same charge as the electron. Apply Bohr atomic model and consider all possible transitions of this hypothetical particle directly to the first excited state. The longest wavelength photon that will be emitted has wavelength (given in terms of Rydberg constant \(R\) for the hydrogen atom) equal to (a) \(\frac{9}{5 R}\) (b) \(\frac{36}{5 R}\) (c) \(\frac{18}{5 R}\) (d) \(\frac{4}{R}\)

To what series does the spectral line of atomic hydrogen belong if its wave number is equal to the difference between the wave numbers of the following two lines of the Balmer series: \(486.1\) and \(410.2 \mathrm{~nm} ?\) (a) Lyman series (b) Balmer series (c) Paschen series (d) Brackett series

If an electron in \(\mathrm{H}\) -atom jumps from one orbit to other, its angular momentum doubles. The distance of electron from nucleus becomes ___times the initial distance. (a) 2 (b) 4 (c) \(\frac{1}{2}\) (d) \(\frac{1}{4}\)

The angular momentum of electron revolving in the second orbit of \(\mathrm{H}\) -atom is ' \(x^{\prime} \mathrm{J} \cdot \mathrm{s}\). The angular momentum of electron in the second orbit of \(\mathrm{He}^{+}\) ion should be (a) \(x \mathrm{~J} \cdot \mathrm{s}\) (b) \(2 x \mathrm{~J} \cdot \mathrm{s}\) (c) \(0.5 x \mathrm{~J} \cdot \mathrm{s}\) (d) \(4 x \mathrm{~J} \cdot \mathrm{s}\)

If the radius of first Bohr orbit is \(x\) unit, then de-Broglie wavelength of electron in the third orbit is (a) \(2 \pi x\) unit (b) \(6 \pi x\) unit (c) \(9 x\) unit (d) \(18 \pi x\) unit

If \(E_{1}, E_{2}\) and \(E_{3}\) are the kinetic energies of an electron, an \(\alpha\) -particle and a proton, with same de-Broglie wavelength, then (a) \(E_{1}>E_{3}>E_{2}\) (b) \(E_{2}>E_{3}>E_{1}\) (c) \(E_{1}>E_{2}>E_{3}\) (d) \(E_{1}=E_{2}=E_{3}\)

A proton and an \(\alpha\) -particle are accelerated through the same potential difference. The ratio of their de-Broglie wavelengths is (a) \(1: 1\) (b) \(2: 1\) (c) \(\sqrt{2}: 1\) (d) \(2 \sqrt{2}: 1\)

As the orbit number increases, the \(\mathrm{K} . \mathrm{E}\). and \(\mathrm{P} . \mathrm{E}\). for an electron: (a) both increases (b) both decreases (c) K.E. increases but P.E. decreases (d) P.E. increases but K.E. decreases

The ratio of energies of first excited state of \(\mathrm{He}^{+}\) ion and ground state of \(\mathrm{H}\) -atom is (a) \(1: 1\) (b) \(4: 1\) (c) \(1: 4\) (d) \(16: 1\)

When accelerated electrons are directed against an anticathode in an X-ray tube, the radiation obtained has a continuous spectrum with a wavelength minimum, \(\lambda_{\min }=\frac{1.24 \times 10^{-6}}{V} \mathrm{~m}\), where \(\mathrm{V}\) is the volt- age used for accelerating the electrons. \(\lambda_{\min }\) for \(V=5 \times 10^{4} \mathrm{~V}\) is (a) \(0.124 \mathrm{~nm}\) (b) \(0.248 \mathrm{~nm}\) (c) \(2.48 \mathrm{~nm}\) (d) \(1.24 \mathrm{~nm}\)

For which atom or ion, the energy level of the second excited state is \(13.6 \mathrm{eV}\) ? (a) \(\mathrm{H}\) (b) \(\mathrm{He}^{+}\) (c) \(\mathrm{Li}^{2+}\) (d) Li

The dynamic mass (in \(\mathrm{kg}\) ) of the photon with a wavelength corresponding to the series limit of the Balmer transitions of the \(\mathrm{He}^{+}\) ion is (a) \(4.22 \times 10^{-36}\) (b) \(2.24 \times 10^{-34}\) (c) \(2.42 \times 10^{-35}\) (d) \(4.22 \times 10^{-35}\)

The ratio of potential energy of electron in the third orbit of \(\mathrm{Li}^{2+}\) ion to the kinetic energy of electron in the fourth orbit of \(\mathrm{He}^{+}\) ion should be (a) \(8: 1\) (b) \(-8: 1\) (c) \(-16: 1\) (d) \(1: 1\)

What should be the increase in kinetic energy, of electron in order to decrease its de-Broglie wavelength from \(100 \mathrm{~nm}\) to \(50 \mathrm{~nm} ?\) (a) \(0.451 \mathrm{keV}\) (b) \(4.51 \times 10^{-4} \mathrm{eV}\) (c) \(4.51 \times 10^{-3} \mathrm{eV}\) (d) \(0.0451 \mathrm{eV}\)

An \(\alpha\) -particle is accelerated from rest through a potential difference of \(6.0 \mathrm{~V}\). Its de-Broglie wavelength is (a) \(5 \AA\) (b) \(4.15 \mathrm{pm}\) (c) \(414.6 \AA\) (d) \(5 \mathrm{~nm}\)

The potential energy of electron revolving in the ground state of \(\mathrm{H}\) atom is (a) \(-13.6 \mathrm{eV}\) (b) \(-6.8 \mathrm{eV}\) (c) \(-27.2 \mathrm{eV}\) (d) Zero

Photoelectrons are liberated by ultraviolet light of wavelength \(3000 \AA\) from a metallic surface for which the photoelectric threshold is \(4000 \AA\). The de-Broglie wavelength of electrons emitted with maximum kinetic energy is (a) \(1000 \AA\) (b) \(42.43 \AA\) (c) \(12.05 \AA\) (d) \(3.54 \AA\)

As the orbit number increases, the difference in two consecutive energy levels (a) remain constant (b) increases (c) decreases (d) is unpredictable

The minimum uncertainty in de-Broglie wavelength of an electron accelerated from rest by a potential difference of \(6.0 \mathrm{~V}\), if the uncertainty in measuring the position is \(\frac{1}{\pi} \mathrm{nm}\), is (a) \(6.25 \AA\) (b) \(6.0 \AA\) (c) \(0.625 \AA\) (d) \(0.3125 \AA\)

The orbital angular momentum of \(2 \mathrm{p}\) and \(3 \mathrm{p}\) -orbitals (a) are same (b) are different, more for 2p-orbital (c) are different, more for 3 p-orbital (d) depends on the type of atom or ion

For which transition in \(\mathrm{H}\) -atom, the amount of energy released will be maximum? (a) \(n=4\) to \(n=2\) (b) \(n=5\) to \(n=2\) (c) \(n=2\) to \(n=1\) (d) \(n=7\) to \(n=2\)

How much energy is needed for an electron revolving in the second orbit of \(\mathrm{He}^{+}\) ion, in order double its angular momentum? (a) \(40.8 \mathrm{eV}\) (b) \(2.55 \mathrm{eV}\) (c) \(10.2 \mathrm{eV}\) (d) \(12.09 \mathrm{eV}\)

If an electron has spin quantum number of \(+1 / 2\) and magnetic quantum number of \(-1\), it cannot be present in (a) s-orbital (b) p-orbital (c) d-orbital (d) f-orbital

An electron revolving round H-nucleus in ground state absorbs \(10.2 \mathrm{eV}\) energy. Its angular momentum increases by (a) \(\frac{h}{2 \pi}\) (b) \(\frac{h}{\pi}\) (c) \(\frac{2 h}{\pi}\) (d) \(\frac{h}{4 \pi}\)

In which of the following orbital, electron will be closer to the nucleus? (a) \(6 \mathrm{~s}\) (b) \(4 \mathrm{f}\) (c) \(5 \mathrm{~d}\) (d) \(6 p\)

In the absence of external magnetic field, d-orbital is (a) 3 -fold degenerate (b) 5 -fold degenerate (c) 7 -fold degenerate (d) non-degenerate

The excitation energy of an electron from second orbit to third orbit of a hydrogenlike atom or ion with +Ze nuclear charge is \(47.2 \mathrm{eV}\). If the energy of \(\mathrm{H}\) -atom in lowest energy state is \(-13.6 \mathrm{eV}\), the value of \(Z\) is (a) 4 (b) 5 (c) 6 (d) 7

Electromagnetic radiations of wavelength \(240 \mathrm{~nm}\) are just sufficient to ionize sodium atom. The ionization energy of sodium (in \(\mathrm{kJ} / \mathrm{mol}\) ) is (a) \(5.167\) (b) \(498.58\) (c) \(118.83\) (d) \(51.67\)

Possible set of quantum numbers for which: \(n=4, l=3\) and \(s=+\frac{1}{2}\) is (a) 14 (b) 7 (c) 5 (d) 10