De Broglie's Hypothesis

Q. The momentum of a particle with de-Broglie wavelength $1\stackrel{\circ }{A}$ is: $(h=6.62\times {10}^{-34}Js)$

1. $6.62\times {10}^{-24}kgm{s}^{-1}$
2. $6.62\times {10}^{-24}kgcm{s}^{-1}$
3. $9.62\times {10}^{-24}kgm{s}^{-1}$
4. $6.62\times {10}^{-22}kgm{s}^{-1}$

Q.

Does Huygens Principle apply to the Sound Waves?

Q. The de-Broglie wavelength associated with a ball of mass 1kg having kinetic energy 0.5 J is

1. $6.626\times {10}^{-34}m$
2. $13.20\times {10}^{-34}m$
3. $10.38\times {10}^{-21}m$
4. $6.626\times {10}^{-34}\stackrel{\circ }{A}$

Q.

Why do electrons have wave properties?

Q.

If vacuum tube is operated at 6.4 kV, what is the wavelength of X-ray produced:-

1. $1.93Ă$

2. $1.53Ă$

3. $2.67Ă$

4. $0.78Ă$

Q.

In the equation ${\mathrm{G}}_{°}={\mathrm{nFE}}_{°\mathrm{cell}}$ F is__________.

Q. The wavelength associated with a golf ball weighing 200 g and moving at a speed of 20 m/h is of the order:

1. $3.97\times {10}^{-10}m$
2. $5.97\times {10}^{-20}m$
3. $5.97\times {10}^{-31}m$
4. $3.97\times {10}^{-31}m$

Q.

A stream of electrons from a heated filament was passed between two charged plates kept at a potential difference V esu. If e and m are charge and mass of an electron, respectively, then the value of $\frac{h}{\lambda }$ (where $\lambda$ is the wavelength associated with electron wave) is given by:

1. 2meV
2. $\sqrt{meV}$
3. $\sqrt{2meV}$
4. meV

Q.

Calculate the mass of a photon with wavelength $3.6\mathring{A}$.

1. $9.1\times {10}^{-29}kg$

2. $8\times {10}^{-29}kg$

3. $7\times$ ${10}^{-27}kg$

4. $6.1\times {10}^{-29}kg$

Q. The French physicist Louis de Broglie in 1924 postulated that matter, like radiation, should exhibit a dual behaviour. He proposed the following relationship between the wavelength lambda of a material particle, its linear momentum p and planck constant h.
$\lambda =\frac{h}{p}=\frac{h}{mv}$
The de Broglie relation implies that the wavelength of a particle should decrease as its velocity increases. It also implies that for a given velocity heavier particles should have shorter wavelength than lighter particles. The waves associated with particles in motion are called matter waves or de Broglie waves. These waves differ from the electromagnetic waves as they
$\left(i\right)$ have lower velocities
$\left(ii\right)$ have no electrical and magnetic fields and
$\left(iii\right)$ are not emitted by the particle under consideration.
The experimental confirmation of the de Broglie’s relation was obtained when Davisson and Germer, in 1927, observed that a beam of electrons is diffracted by a nickel crystal. As diffraction is a characteristic property of waves, hence the beam of electron behaves as a wave, as proposed by de Broglie.

Using Bohr’s theory, the transition, so that the electron's de-Broglie wavelength becomes 3 times of its original value in $H{e}^{+}$ ion will be?

1. $2⟶6$
2. $2⟶4$
3. $1⟶4$
4. $1⟶6$

Q. If $E_e,E_{\alpha },E_p$ represents the kinetic energies of an electron, alpha particle and a proton respectively, each moving with same de-Broglie wavelength then:

1. $E_e=E_{\alpha }=E_p$
2. $E_e>E_{\alpha }>E_p$
3. $E_{\alpha }>E_p>E_e$
4. $E_e>E_p>E_{\alpha }$

Q. Which of the following particles has the largest wavelength? Assume all particles have the same velocity.

1. $C{O}_2$
2. $N{H}_3$
3. Electron
4. Proton

Q. The de broglie wavelength of an electron (initially at rest) accelerated by an electric potential of 9 volts is given by:
Given: $m_e=9.1\times {10}^{-31}kg,e=1.6\times {10}^{-19}C,$
$h=6.6\times {10}^{-31}Js$

1. 0.87 nm
2. 0.62 nm
3. 0.41 nm
4. 0.14 nm

Q. Which of the following particles has the largest wavelength? Assume all particles have the same velocity.

1. $C{O}_2$
2. $N{H}_3$
3. Electron
4. Proton

Q.

If the velocity of hydrogen molecule is $5\times {10}^{4}cmse{c}^{-1}$, then its de-Broglie wavelength is

1. $2\mathring{A}$

2. $4\mathring{A}$

3. $8\mathring{A}$

4. $100\mathring{A}$

Q. The momentum of a particle with de Broglie wavelength $2\stackrel{\circ }{A}$ is:
$(\text{Planck's constant},h=6.62\times {10}^{-34}Js)$

1. $3.31\times {10}^{-24}kgm{s}^{-1}$
2. $3.31\times {10}^{-24}kgcm{s}^{-1}$
3. $9.62\times {10}^{-24}kgm{s}^{-1}$
4. $6.62\times {10}^{-22}kgm{s}^{-1}$

Q. An electron travels with a velocity of $xm{s}^{-1}$. For a proton to have the same de-Broglie wavelength, the velocity will be approximately:

1. $\frac{1840}{x}$
2. $\frac{x}{1840}$
3. $1840x$
4. $x$

Q. The dynamic mass of a photon having a wavelength of 10 nm is:

1. $2.21\times {10}^{-35}kg$
2. $2.21\times {10}^{-34}kg$
3. $2.21\times {10}^{-33}kg$
4. $2.21\times {10}^{-32}kg$

Q. Calculate the wavelength associated with an electron moving with a velocity of ${10}^{10}cm/s.$

1. $0.072\stackrel{\circ }{A}$
2. $0.829\stackrel{\circ }{A}$
3. $0.667\stackrel{\circ }{A}$
4. $1.009\stackrel{\circ }{A}$

Q. Uncertainity in position is twice the uncertainity in momentum uncertainity in velocity is :

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

Q. The de Broglie wavelength of a sand grain weighing 2 mg blown by a wind of 10 m/s is:

1. $3.31\times {10}^{-29}m$
2. $1.12\times {10}^{-29}m$
3. $2.21\times {10}^{-29}m$
4. $4.42\times {10}^{-29}m$

Q. $13.6eV$ is needed for ionisation of a hydrogen atom. An electron in a hydrogen atom in its ground state absorbs $1.50$ times as much energy as the minimum energy required for it to escape from the atom. What is the wavelength and velocity of the emitted electron?

1. $v=4.0\times {10}^{6}m/s;\lambda =4.7\times {10}^{-10}m$
2. $v=1.55\times {10}^{6}m/s;\lambda =4.7\times {10}^{-10}m$
3. $v=1.55\times {10}^{6}m/s;\lambda =16.0\times {10}^{-12}m$
4. $v=4.0\times {10}^{6}m/s;\lambda =16.0\times {10}^{-12}m$

Q. The kinetic energy of an electron is $9.1\times {10}^{-25}J$. Calculate the de Broglie wavelength for the same.
$(\text{Planck's constant},h=6.6\times {10}^{-34}Js,\text{mass of electron}=9.1\times {10}^{-31}kg)$

1. $0.51\times {10}^{-5}m$
2. $0.51\times {10}^{-6}m$
3. $0.51\times {10}^{-7}m$
4. $0.51\times {10}^{-8}m$

Q. Calculate the number of photons emitted per second by a $10\text{W}$ sodium vapour lamp. Assume that $60\%$ of the consumed energy is converted into light. Wavelength of sodium light is $662\text{nm}$.
(Given that $h=6.62\times {10}^{-34}\text{J s}$)

1. $2\times {10}^{19}$
2. $3\times {10}^{19}$
3. $2\times {10}^{20}$
4. $3\times {10}^{20}$

Q. An electron travels with a velocity of x $m{s}^{-1}$. For a proton to have the same de-broglie wavelength, the approximate velocity should be:
(Given, $\frac{m_p}{m_e}=1840)$

1. $\frac{1840}{x}$
2. $\frac{x}{1840}$
3. 1840 x
4. x

Q. The de Broglie wavelength of electron in the second orbit of Li${}^{2+}$ ion will be equal to the de Broglie wavelength of electron in

1. n = 3 of H atom
2. n = 4 of C${}^{5+}$ ion
3. n = 6 of Be${}^{3+}$ ion
4. n = 3 of He${}^{+}$ ion

Q. When a light of wavelength ${}^{\prime }{\lambda }^{\prime }$ falls on the surface of a metal with threshold wavelength ${}^{\prime }{\lambda }_0^{\prime }$, an electron of mass '2m' is emitted. The de Broglie wavelength of emitted electron is:

1. ${\left[\frac{h\left(\lambda {\lambda }_0\right)}{4mc({\lambda }_o-\lambda )}\right]}^{\frac{1}{2}}$
2. ${\left[\frac{h\left(\lambda {\lambda }_0\right)}{2mc(\lambda -{\lambda }_0)}\right]}^{\frac{1}{2}}$
3. ${\left[\frac{h\lambda {\lambda }_0}{2mc}\right]}^{\frac{1}{2}}$
4. ${\left[\frac{h(\lambda -{\lambda }_0)}{2mc\left(\lambda {\lambda }_0\right)}\right]}^{\frac{1}{2}}$

Q. If the kinetic energy (K.E.) of an electron is $2.5\times {10}^{–24}\text{J}$, calculate its de-Broglie wavelength.

1. 400 nm
2. 380 nm
3. 311 nm
4. 298 nm

Q. Calculate the wavelength (in nanometer) associated with a proton moving at $1.0\times {10}^{3}m{s}^{-1}$
$(\text{Mass of proton}=1.67\times {10}^{-27}kg$)
$\left(\text{Planck's constant}\right(h)=6.63\times {10}^{-34}Js)$

1. 0.40 nm
2. 1.5 nm
3. 10.0 nm
4. 2.3 nm

Q. The vapours of $Hg$ absorb some electrons accelerated by a potential difference of $9.0\text{eV}$, as a result of which, light is emitted. If the 25% of energy of a single incident electron is supposed to be converted into light emitted by a single $Hg$ atom, find the wave number $\frac{1}{\lambda }$ of the light.

(Take: Planck's constant (h) =$6.6\times {10}^{-34}Js$)

1. $3.63\times {10}^6{\text{m}}^{-1}$
2. $1.82\times {10}^6{\text{m}}^{-1}$
3. $3.63\times {10}^9{\text{m}}^{-1}$
4. $1.82\times {10}^9{\text{m}}^{-1}$