De Broglie's Hypothesis

Q.

What is the dimensional formula of Plancks constant?

Q.

The mass of an electron is 9.1 × ${10}^{–31}$ kg. If its K.E. is 3.0 × ${10}^{–25}$ J, calculate its wavelength.

Q.

A proton and an alpha - particle are accelerated through same potential difference. Then, the ratio of de-Broglie wavelength of proton and alpha-particle is:

1. $\sqrt{2}$

2. $\frac{1}{\sqrt{2}}$

3. $2\sqrt{2}$

4. None of these

Q.

State and explain wave-particle duality?

Q.

Calculate the wavelength of an electron moving with a velocity of 2.05 × ${10}^{7}m{s}^{–1}$.

Q.

The electronic spectrum of ${\left[\mathrm{Ti}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{+3}$ shows a single broad peak with a maximum at $20,300{\mathrm{cm}}^{-1}$. The crystal field stabilization energy (CFSE) of the complex ion, in $\mathrm{kJ}\mathrm{mol}-1$, is:

1. $83·7$

2. $242·5$

3. $145·5$

4. $97$

Q. If proton, electron and $\alpha$-particle are moving with same kinetic energy then the order of their de-broglie's wavelength.

1. ${\lambda }_p>{\lambda }_e>{\lambda }_{\alpha }$
2. ${\lambda }_{\alpha }>{\lambda }_p>{\lambda }_e$
3. ${\lambda }_{\alpha }<{\lambda }_p<{\lambda }_e$
4. ${\lambda }_e={\lambda }_p<{\lambda }_{\alpha }$

Q. what is the difference between Ψ and Ψ^2 ?

Q. The de Broglie wavelength of a tennis ball of mass 60 g moving with a velocity of $\text{10}m/s$ is approxiamately: $\text{(plancks's constant,}h=6.63\times {10}^{-34}Js)$

1. ${10}^{-25}m$
2. ${10}^{-33}m$
3. ${10}^{-31}m$
4. ${10}^{-16}m$

Q.

The de Broglie wavelength of a particle with mass 1 gram and velocity 100 m/sec is

1. 6.63 × 10^-33 m

2. 6.63 × 10^-34 m

3. 6.63 × 10^-35 m

4. 6.65 × 10^-35 m

Q.

The mass of a photon with wavelength 3.6˚A is .

1. 9.1 × ${10}^{-29}Kg$
2. 6.1 × ${10}^{-29}Kg$
3. 8 × ${10}^{-29}Kg$

Q. The kinetic energy of an electron is $4.55\times {10}^{-25}J$. Calculate the de Broglie wavelength for the same.
$h=6.6\times {10}^{-34}Js,\text{mass of electron}=9.1\times {10}^{-31}kg$

1. $0.72\times {10}^{-5}m$
2. $0.72\times {10}^{-6}m$
3. $0.72\times {10}^{-8}m$
4. $0.72\times {10}^{-7}m$

Q. The approximate wavelength associated with a gold ball weighing 200 gm and moving at a speed of 5 m/h is in the order of ?

1. ${10}^{-1}m$
2. ${10}^{-20}m$
3. ${10}^{-30}m$
4. ${10}^{-40}m$

Q. Find the de Broglie wavelength (in m) of an electron moving in the first Bohr orbit of hydrogen.

1. $3.34\times {10}^{-10}$
2. $8.34\times {10}^{-9}$
3. $5.34\times {10}^{-10}$
4. $6.34\times {10}^{-9}$

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.

The work function of some metals is listed below how many of these metals show the Photoelectric effect when the light of $300\mathrm{nm}$ wavelength falls on them?

Metal	K	Na	Li	Mg	Ag	Fe	W	Cu	Pt
ϕ (eV)	2.2	2.3	2.4	3.7	4.3	4.7	4.75	4.8	6.3

1. Two

2. Four

3. Five

4. None of these

Q.

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

1. 8 Å

2. 100 Å

3. 2 Å

4. 4 Å

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

Q. If uncertainty in position and velocity are equal, then uncertainty in momentum will be

1. 
2. 
3. 
4. 

Q.

Question 16

If travelling at same speeds, which of the following matter waves have the shortest wavelength ?

(a) Electron (b) Alpha particle $\left(H{e}^{2+}\right)$ (c) Neutron (d) Proton

Q.

What is the mass of photon in motion?

Q.

If the velocity of the electron in Bohr’s first orbit is 2.19 × ${10}^6$ m$s^{–1}$, calculate the de Broglie wavelength associated with it.

Q. The de Broglie wavelength of an electron moving in a circular orbit is $\lambda .$ The minimum radius of orbit is:

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

Q. Wave mechanical model of the atom depends upon?

1. De-Broglie concept of dual nature of electron
2. Schrodinger uncertainty principle
3. All
4. Heisenberg uncertainty principle

Q.

The velocity of matter waves is _____________.

Q.

A proton, a deuteron and an $\alpha$ particle having same momentum enter a uniform magnetic field at right angles to the field. The ratio of their angular momentum with respect to their corresponding centres during their motion in the magnetic field is

1. 2:1:3

2. 4:1:2

3. 4:2:1

4. 2:2:1

Q. The atomic masses of 'He' and 'Ne' are 4 and 20 amu respectively. The value of the de Broglie wavelength of 'He' gas at $-{73}^{\circ }C$ is 'M' times that of de Broglie wavelength of Ne at $+{727}^{\circ }C$. Assuming that Kinetic energy is proportional to absolute temperature, 'M' is

Q. If the kinetic energy of an electron is increased 4 times, the wavelength of the de Broglie wave associated with it would become

1. 4 times
2. 0.5 times
3. 0.25 times
4. 2 times

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. 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