Dual Nature of Radiation and Matter Test

Result

Dual Nature of Radiation and Matter Test - 74

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Weekly Quiz Competition

Question 1
1 / -0

An electron of mass m and a photon have same energy E.The ratio of de-Broglie wavelengths associated with them is

A
$$\frac { 1 }{ c } \left( \frac { 2m }{ E } \right) ^{ \frac { 1 }{ 2 } }$$

B
$$\frac { 1 }{ c } \left( \frac { E }{ 2m } \right) ^{ \frac { 1 }{ 2 } }$$

C
$$\left( \frac { E }{ 2m } \right) ^{ \frac { 1 }{ 2 } }$$

D
$$C\left( 2mE \right) ^{ \frac { 1 }{ 2 } }$$

Solution
Question 2
1 / -0

What should be the ratio of the energies of radiations whose wavelengths are $$3000 \mathring { A }$$ and $$6000 \mathring { A }$$ ?

A
$$1:2$$

B
$$2:1$$

C
$$1:3$$

D
$$3:4$$

Solution

Area of a sector $$=\cfrac{radian}{2\pi}\times (\pi {r}^{2})$$
$$\cfrac { \cfrac { 11 }{ 6 } \pi }{ 2\pi } \times \pi { r }^{ 2 }=33\pi$$
$$\pi { r }^{ 2 }$$ area of circle (A)
$$\cfrac{11}{12}\times A=33\pi$$
$$A=\cfrac{33\times 12}{11}\pi$$
$$A=36\pi$$ unit square is area of circle
Question 3
1 / -0

Mass of a photon with wavelength $$3.6A^{o}$$ moving with velocity of light is

A
$$9.1\times 10^{-31}\ kg$$

B
$$6.1\times 10^{-29}\ kg$$

C
$$9.1\times 10^{-28}\ kg$$

D
$$6.1\times 10^{-31}\ kg$$

Solution
Question 4
1 / -0

An $$\alpha$$ -particle is accelerated through a potential difference of V volts from rest.The de-Broglie's was associated with it is-

A
$$\sqrt { \frac { 150 }{ V } } { A }^{ o }$$

B
$$\frac { 0.286 }{ \sqrt { V } } { A }^{ o }$$

C
$$\frac { 0.101 }{ \sqrt { V } } { A }^{ o }$$

D
$$\frac { 0.983 }{ \sqrt { V } } { A }^{ o }$$

Solution

The potential energy due to potential difference $$V$$ will provide Kinetic energy to $$\alpha-$$particle.
Mass of $$\alpha-$$ particle $$=4\times1.67\times10^{-27}kg= 6.68\times10^{-27}kg$$
Charge of $$\alpha-$$ particle $$=2\times1.6\times10^{-19}C = 3.2\times10^{-19}C$$
$$\dfrac12mv^2 = qV$$

$$v = \sqrt{\dfrac{2qV}{m}} = \sqrt{\dfrac{2\times 3.2\times10^{-19}V}{6.68\times10^{-27}}}= 0.978\times10^4\sqrt{V}$$ $$m/s$$

de-Broglie wavelength is, $$\lambda =\dfrac{h}{p} = \dfrac{h}{mv}$$

$$\lambda = \dfrac{6.6\times10^{-34}}{6.68\times10^{-27}\times 0.978\times10^4\sqrt{V}}$$

$$\lambda = \dfrac{0.101}{\sqrt{V}} $$
Question 5
1 / -0

With what velocity must an electron travel so that its momentum is equal to that of a photon of wavelength $$\lambda$$ = 5200$$\overset { \circ }{ A } $$?

A
1400 m$$s^{-1}$$

B
140 m$$s^{-1}$$

C
14 m$$s^{-1}$$

D
1.4 m$$s^{-1}$$

Solution
Question 6
1 / -0

Light of frequency $$7.21 \times {10^{14}}Hz$$ is incident on a metal surface. The maximum speed of the photoelectrons emitted is $$6.0 \times {10^5}m\,{s^{ - 1}}$$. what is the threshold frequency for the photoemission of electrons?

A
$$4.73 \times {10^{14}}Hz$$

B
$$7.31 \times {10^{14}}Hz$$

C
$$4.73 \times {10^{15}}Hz$$

D
$$7.34 \times {10^{15}}Hz$$

Solution
Question 7
1 / -0

Sodium and copper have work functions 2.3 eV and 4.5 eV respectively. Then the ratio of the wavelengths . nearest to-

A
1 : 2

B
4 : 1

C
2 : 1

D
1 : 4
Question 8
1 / -0

What should be the approximate K.E. of an electron so that its de -Broglie wavelength is equal to the wavelength of x -ray of maximum energy produced in an x -ray tube operating at 24,800 V? $$(h = 6.6 /\times 10^{-34}J - sec$$, mass of electron $$m =9.1 \times 10^{-31} kg)$$ (give answer in $$10^2 eV).$$

A
$$3$$

B
$$4$$

C
$$6$$

D
$$9$$

Solution
Question 9
1 / -0

If the first Bohr's orbit of hydrogen is $$r_{ \circ },$$ the de-Broglie wavelength of electron in $${ 3 }^{ rd }$$ orbit $$He^{ + }$$ is about

A
$${ 9r }_{ \circ }$$

B
$$\dfrac { { 9r }_{ \circ } }{ 2 } $$

C
$${ 3\pi r }_{ \circ }$$

D
$${ 6\pi r }_{ \circ }$$

Solution
Question 10
1 / -0

Find the velocity of electrons liberated by electromagnetic radiation of wavelength $$ \lambda =18.0$$ nm from stationary $$He^+$$ ions in the ground state.

A
$$2.3 \times 10^6$$ m/s

B
$$2 \times 10^6$$ m/s

C
$$2 \times 10^3$$ m/s

D
none of these

Solution