Hydrogen Spectra

Q. The ground state energy of hydrogen atom is –13.6 eV. What are thekinetic and potential energies of the electron in this state?

Q. What is the shortest wavelength present in the Paschen series ofspectral lines?

Q. The energy that should be added to an electron to reduce its de Broglie wavelength from 1 nm to 0.5 nm is

1. Four times the initial energy

2. Equal to the initial energy

3. Twice the initial energy

4. Thrice the initial energy

Q. In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is

1. $\frac{5}{27}$
2. $\frac{4}{9}$
3. $\frac{9}{4}$
4. $\frac{27}{5}$

Q. Energy required to excite an electron from second to third Bohr orbit of a Hydrogen like atom is 47.2 eV, then

1. Z = 6
2. Z = 5
3. Wavelength of radiation required to excite an electron from ground state to infinity is 36.4 $\stackrel{o}{A}$
4. Radius of 1st Bohr orbit is 10.6 pm

Q. The Lyman series of hydrogen spectrum lies in the region

1. Infrared
2. Of X - rays
3. Ultraviolet
4. Visible

Q.

A particle is travelling, $4$ times as fast as an electron. Assuming the ratio of the de-Broglie wavelength of a particle to that of the electron is $2:1$, the mass of the particle is

1. $1/16$ times of mass of electron

2. $1/6$ times the mass of electron

3. $1/8$ times the mass of electron

4. $8$ times the mass of electron

Q. Which one of the series of hydrogen spectrum is in the visible region

1. Balmer series
2. Bracket series
3. Lyman series
4. Paschen series

Q. Calculate the shortest wavelength of the spectral lines emitted in Balmer series.[Given Rydberg constant, R=${10}^7{m}^{-l}$]

Q. As per Bohr’s model, which of the following cannot be angular momentum of an electron in hydrogen atom?

1. $\frac{h}{\pi }$
2. $\frac{3h}{2\pi }$
3. $\frac{h}{4\pi }$
4. $\frac{2h}{\pi }$

Q. A radioactive element emits 200 particles per second. After three hours 25 particles per second are emitted. What will be the half-life period of this element?

1. 50 $min$
2. 60 $min$
3. 70 $min$
4. 80 $min$

Q.

The shortest wavelength Of ${\mathrm{He}}^{+}$ ion in the Balmer Series is x, then the longest wavelength in the Paschen Series Of ${\mathrm{Li}}^{+2}$ Is:

Q. When an electron in hydrogen atom jumps from the third excited state to the ground state, how would the de-Broglie wave length associated with the electron change? Justify your answer.

Q.

Is energy directly proportional to frequency?

Q. If $10\text{\%}$ of the electrical energy supplied to an incandescent light is radiated as visible light, the number of photons emitted by a $60\text{W}$ bulb per second is $1.8\times {10}^{9.5k}$. The value of $k$ is(Integer only) $(\lambda =6000\dot{A})$

Q. The ratio of wave length of first line of Lyman series to the first line of Balmer series is

1. 1 : 4
2. 5 : 27
3. 27 : 20
4. 20 : 27

Q. The wavelength associated with an electron accelerated through a potential difference of 100 V is nearly

1. 100 Å

2. 123 Å

3. 1.23 Å
4. 0.123 Å

Q. An electron makes a transition from $n=2$ to $n=1$ state in a hydrogen like atom.
Choose the correct statements.

1. Magnetic field at the site of nucleus is decreased by $16$ times
2. Magnetic field at the site of nucleus is increased by $32$ times
3. Angular momentum of electron is decreased
4. Angular momentum of electron is increased

Q. Which of the following is true

1. Paschen series is a line spectrum in the infrared
2. Lyman series is a continuous spectrum
3. Balmer series is a line spectrum in the ultraviolet
4. The spectral series formula can be derived from the Rutherford model of the hydrogen atom

Q. The transition from the state n = 4 to n = 3 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition.

1. $4\to 2$
2. $5\to 4$
3. $3\to 2$
4. $2\to 1$

Q. Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $r={\lambda }_1/{\lambda }_2$, is given by

1. $r=\frac{1}{3}$
2. $r=\frac{4}{3}$
3. $r=\frac{2}{3}$
4. $r=\frac{3}{4}$

Q. PARAGRAPH
In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $\left[E\right]$ and [𝐵] stand for dimensions of electric and magnetic fields respectively, while $\left[{\epsilon }_0\right]$ and $\left[{\mu }_0\right]$ stand for dimensions of the permittivity and permeability of free space respectively. $\left[L\right]$ and $\left[T\right]$ are dimensions of length and time respectively. All the quantities are given in SI units.

The relation between $\left[{\epsilon }_0\right]$ and $\left[{\mu }_0\right]$ is

1. $\left[{\mu }_0\right]=\left[{\in }_0\right]\left[L{]}^2\right[T{]}^{-2}$
2. $\left[{\mu }_0\right]=\left[{\in }_0\right]\left[L{]}^{-2}\right[T{]}^2$
3. $\left[{\mu }_0\right]=\left[{\in }_0{]}^{-1}\right[L{]}^2[T{]}^{-2}$
4. $\left[{\mu }_0\right]=\left[{\in }_0{]}^{-1}\right[L{]}^{-2}[T{]}^2$

Q. Which of the following is not true about the Bohr's model of atoms?

1. It assumes that the angular momentum of electrons is quantized.
2. It uses Einstein's photoelectric equations.
3. It predicts continuos emission spectra for atoms.
4. It predicts the same emission spectra for all types of atoms.

Q. Estimate the wavelength at which plasma reflection will occur for a metal having the density of electrons $N\approx 4\times {10}^{27}{m}^{-3}$. Take ${\epsilon }_0\approx {10}^{-11}\text{and}m\approx {10}^{-30},$ where these quantities are in proper SI units

1. 200 nm
2. 600 nm
3. 800 nm
4. 300 nm

Q. The energy levels of the hydrogen spectrum is shown in figure. There are some transitions A, B, C, D and E. Transition A, B and C respectively represent

1. First member of Lyman series, third spectral line of Balmer series and the second spectral line of Paschen series
2. Ionization potential of hydrogen, second spectral line of Balmer series and third spectral line of Paschen series
3. Series limit of Lyman series, third spectral line of Balmer series and second spectral line of Paschen series
4. Series limit of Lyman series, second spectral line of Balmer series and third spectral line of Paschen series

Q. In the spectrum of hydrogen atom, ratio of the longest wavelength in Lyman series to the longest wavelength in Balmer series is:

1. $\frac{5}{27}$
2. $\frac{4}{9}$
3. $\frac{3}{2}$
4. $\frac{1}{93}$

Q. The following can be arranged in decreasing order of wave number as
$A$. Radio wave
$B$. Microwave
$C$. X-Ray
$D$. Visible Ray

1. $A>B>D>C$
2. $C>D>B>A$
3. $A>B>C>D$
4. $D>C>B>A$

Q.

A parallel beam of light of wavelength 100 nm passes through a sample of atomic hydrogen gas in fground state.

(a) Assume that when a photon supplies some of its energy to a hydrogen atom, the rest of the energy appears as another photon moving in the direction of the incident photon. Neglecting the light emitted by the excited hydrogen atoms in the direction of the incident beam, , what wavelengths may be observed in the transmitted beam ?

(b) A radition detector is placed near the gas to detect radition coming perpendicular to the incident beam. Find the wavelengths of raditions that may be detected by the detector.

Q. The radio of the velocity of sound in Hydrogen gas $(\gamma =7/5)$ to that in Helium gas $(\gamma =5/3)$ at the same temperature is $\frac{\sqrt{21}}{5}$.

1. True
2. False

Q. In $L{i}^{++}$, electron in first Bohr orbit is excited to a level by a radiation of wavelength $\lambda$. when the ion gets deexcited to the ground state in all possible ways (including intermediate emissions), a total of six spectral lines are observed. What is the value of $\lambda$ ?
(Given : $h=6.63\times {10}^{34}Js$; $c=3\times {10}^{8}m{s}^{-1}$)

1. $9.4nm$
2. $12.3nm$
3. $10.8nm$
4. $11.4nm$