The De Broglie Explanation

Q. The wavelength ${\lambda }_e$ of an electron and λp of a photon of same energy E are related by -

1. ${\lambda }_e^2\propto {\lambda }_p$
2. ${\lambda }_p\propto {\lambda }_e$
3. ${\lambda }_p\propto \sqrt{{\lambda }_e}$
4. ${\lambda }_p\propto \sqrt{{\lambda }_e}$

Q.

Calculate the wavelength of the first line in the Lyman series of the hydrogen spectrum ($\mathrm{R}=109677{\mathrm{cm}}^{-1}$) how to do this?

Q. An electron moving with speed $v$ and a photon, moving with speed $c$, have the same de-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is :

1. $\frac{v}{3c}$
2. $\frac{2c}{v}$
3. $\frac{v}{2c}$
4. $\frac{3c}{v}$

Q. If the kinetic energy of the particle is increased to 16 times its previous value, the percentage change in the de-Broglie wavelength of the particle is

1. 25
2. 75
3. 60
4. 50

Q. What is the de Broglie wavelength of an electron with a kinetic energy of $120\text{eV}$?
(Given: $h=6.63\times {10}^{-34}\text{Js},m_e=9.11\times {10}^{-31}\text{kg},e=1.6\times {10}^{-19}\text{coulomb}$

1. $725\text{pm}$
2. $500\text{pm}$
3. $322\text{pm}$
4. $112\text{pm}$

Q.

If ${\lambda }_1$ and ${\lambda }_2$ are the wavelengths of the third member of Lyman and the first member of the Paschen series respectively, then the value of ${\lambda }_1:{\lambda }_2$ is

1. $1:3$

2. $1:9$

3. $7:135$

4. $7:108$

Q. The energy of a photon is equal to the kinetic energy of a proton. The energy of the photon is E. Let ${\lambda }_1$ be the de-Broglie wavelength of the proton and ${\lambda }_2$ be the wavelength of the photon. The ratio ${\lambda }_1/{\lambda }_2$ is proportional to

1. $E^{-1}$
2. $E^0$
3. $E^{1/2}$
4. $E^{-2}$

Q. The ratio of minimum to maximum wavelength of radiation emitted by transition of an electron, to ground state of Bohr's hydrogen atom is,

1. $\frac{3}{4}$
2. $\frac{1}{4}$
3. $\frac{1}{8}$
4. $\frac{3}{8}$

Q. Which of the following has the largest de Broglie wavelength assuming that the velocity is the same for all?

1. electron
2. proton
3. $C{O}_2$ molecule
4. $N{H}_3$ molecule

Q. The largest wavelength in the ultraviolet region of the hydrogen spectrum is $122\text{nm}$. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is

1. $802\text{nm}$
2. $823\text{nm}$
3. $1882\text{nm}$
4. $1648\text{nm}$

Q. A 12.5 eV electron beam is used to excite a gaseous hydrogen atom at room temperature. Determine the wavelengths and the corresponding series of the lines emitted.

Q. The wavelength of the first spectral line in the Balmer series of hydrogen atom is $6561\dot{\text{A}}.$ The wavelength of the second spectral line in the Balmer series of single ionized helium atom is ____ $\dot{\text{A}}$.

Q. If the deBroglie wavelength of an electron is equal to ${10}^{-3}$ times the wavelength of a photon of frequency $6\times {10}^{14}\text{Hz},$ then the speed of an electron is equal to:
$\text{(Speed of light,}c=3\times {10}^8{\text{ms}}^{-1}\text{Planck's constant,}h=6.63\times {10}^{-34}\text{Js}\text{Mass of electron,}{m}_e=9.1\times {10}^{-31}\text{kg})$

1. $1.1\times {10}^6{\text{ms}}^{-1}$
2. $1.7\times {10}^6{\text{ms}}^{-1}$
3. $1.8\times {10}^6{\text{ms}}^{-1}$
4. $1.45\times {10}^6{\text{ms}}^{-1}$

Q.

What is the quantum effect?

Q. A photon has kinetic energy E = 100 keV which is equal to that of a proton. The wavelength of photon is ${\lambda }_2$ and that of proton is ${\lambda }_1.$ The ratio of ${\lambda }_2/{\lambda }_1$ is proportional to

1. $E^2$
2. $E^{-1/2}$
3. $E^{-1}$
4. $E^{1/2}$

Q.

What is the speed of electron in the second Bohr's orbit of Hydrogen atom? $(Take{v}_0=2.2\times {10}^{6}m/s)$.

1. 

2. 

3. 

4. 

Q.

According to De Broglie 2$\pi$r=n$\lambda$ where n is the quantum number of an orbit, in visual representation of an electron as a wave, n stands for:

1. No. of loops , where one loop is one wavelength

2. No. of electrons

3. No. of half wavelengths

4. Can not comment

Q.

For the Balmer series in the spectrum of H-atom, $\mathrm{v}={\mathrm{R}}_{\mathrm{H}}\left[(1/\mathrm{n}{1}^2)-(1/\mathrm{n}{2}^2)\right]$ The correct statements among (A) to (D) are:

I) The integer ${\mathrm{n}}_1=2$

II) The ionization energy of hydrogen can be calculated from the wave number of these lines.

III) The lines of longest wavelength correspond to ${\mathrm{n}}_2=3$.

IV) As wavelength decreases, the lines of the series converge.

1. II, III, IV

2. I, II, IV

3. I, III, IV

4. I, II, III

Q. The de Brogile wavelength of the electron in the ground state of the hydrogen atom is (Radius of the first orbit of hydrogen atom = $0.53\stackrel{\circ }{A}$

1. $3.33\stackrel{\circ }{A}$
2. $106\stackrel{\circ }{A}$
3. $1.67\stackrel{\circ }{A}$
4. $0.53\stackrel{\circ }{A}$

Q. What is the de Broglie wavelength of (a) a bullet of mass 0.040 kg travelling at the speed of 1.0 km/s, (b) a ball of mass 0.060 kg moving at a speed of 1.0 m/s, and (c) a dust particle of mass 1.0 × 10–9 kg drifting with a speed of 2.2 m/s?

Q. The kinetic energy of an electron is $5\text{eV}$. Calculate the de-Broglie wavelength associated with it. $(h=6.6\times {10}^{-34}\text{Js},m_e=9.1\times {10}^{-31}\text{kg})$

1. $5.47\mathring{\text{A}}$
2. $10.9\mathring{\text{A}}$
3. $2.7\mathring{\text{A}}$
4. $\text{None of these}$

Q. The circumference of first orbit of hydrogen atom is ‘s’. Then the Broglie wavelength of electron in that orbit is

1. 2S
2. S
3. 3S
4. $\frac{S}{2}$

Q. What is a point mass?

Q. Suppose the potential energy for a system of an electron and a proton separated by a distance $r$ is given by $\frac{-k{e}^2}{3r^3}$. Assume Bohr's Atomic Model is applicable. Then -

1. Total energy in the $n^{\text{th}}$ orbit is proportional to $n^6$
2. Total energy in the $n^{\text{th}}$ orbit is proportional to $m^{-3}$ $(m$ is mass of electron$)$
3. Total energy in the $n^{\text{th}}$ orbit is proportional to $n^{-2}$
4. Total energy in the $n^{\text{th}}$ orbit is proportional to $m^3$ $(m$ is mass of electron$)$

Q.

The circumference of the second orbit of an atom or ion having a single electron is $4\times {10}^{-9}\mathrm{m}$ The de-Broglie wavelength of electrons revolving in this orbit should be

1. $1\times {10}^{-9}\mathrm{m}$

2. $2\times {10}^{-9}\mathrm{m}$

3. $4\times {10}^{-9}\mathrm{m}$

4. $8\times {10}^{-9}\mathrm{m}$

Q. The de-Broglie wavelength of an electron in first orbit of Bohr's hydrogen is equal to

1. radius of the orbit
2. perimeter of the orbit
3. diameter of the orbit
4. half of the perimeter of the orbit

Q. The kinetic energy of an electron is $5eV$. Calculate the de-Broglie wavelength associated with it.
($h=6.6\times {10}^{-34}J-s,m_e=9.1\times {10}^{-31}kg$)

1. $5.47\mathring{A}$
2. $10.9\mathring{A}$
3. $2.7\mathring{A}$
4. None of these

Q. Suppose the potential energy between electron and proton at a distance $r$ is given by $\frac{k{e}^2}{3r^3},$ where $k$ is constant. Then using Bohr's theory to hydrogen atom, which of the following is correct

1. Energy in the $n^{th}$ orbit is propotional to $n^6$
2. Energy is proportional to $m^{-3}$ ($m=$ mass of electron)
3. Energy in the $n^{th}$ orbit is proportional to $n^{-2}$
4. Energy is proportional to $m^3$ ($m=$ mass of electron)

Q.

In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of $7.5\times {10}^{-12}\mathrm{m}$, the minimum electron energy required is close to :

1. $1\mathrm{keV}$

2. $25\mathrm{keV}$

3. $500\mathrm{keV}$

4. $100\mathrm{keV}$

Q. The wavelength of de-Broglie wave is $2\mu \text{m}$, then its momentum is, $h=6.63\times {10}^{-34}\text{J-s}$

1. $3.315\times {10}^{-28}\text{kg-m/s}$
2. $1.66\times {10}^{-28}\text{kg-m/s}$
3. $4.97\times {10}^{-28}\text{kg-m/s}$
4. $9.9\times {10}^{-28}\text{kg-m/s}$