Dual Nature of Radiation and Matter Test

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Dual Nature of Radiation and Matter Test - 20

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Question 1
1 / -0

According to Heisenberg's uncertainty principle, which of the following statement is true ?

A
electrons are too small to be studied.

B
every photon is exactly the same size.

C
the more you know about the momentum of an electron, the less you can know about its position.

D
the more you know about the energy of a photon, the less you can know about its frequency.

E
you cannot state with accuracy the number of electrons in atom.

Solution

Heisenberg uncertainty principle states that it is impossible to determine the exact position and the exact momentum of the particle simultaneously.
According to Heisenberg uncertainty principle, $$\Delta x.\Delta p \geq \dfrac{h}{4\pi}$$
Thus lesser the error in the momentum, more will be the error in the position of the particle.
Question 2
1 / -0

Identify the statement which best define the uncertainty principle?

A
We cannot know for certain when any given radioactive particle will undergo decay

B
We cannot know both the momentum and the position of a particle at the same time

C
The laws of physics are the same in all intertial reference frames

D
Light exhibits both wave and particle properties

E
An unobserved particle can be in two places at the same time

Solution

Heisenberg uncertainty principle states that it is impossible to know the exact momentum and the exact position of particle at the same instant.
If we precise the value of position of the particle, then there will be large uncertainty in the value of its velocity (momentum) and vice-versa.
According to uncertainty principle, $$\Delta p. \Delta x \geq \dfrac{h}{4\pi}$$
Question 3
1 / -0

By means of the diffraction experiment, it is determined that the electron's de Broglie wavelength is $$6.6 \times {10}^{-10} m$$. What is the electron's linear momentum? Use Planck's constant, $$h = 6.6 \times {10}^{-34} J{A} s$$.

A
$$1.0 \times {10}^{-44} kg\, {A} {m}/{s}$$

B
$$1.0 \times {10}^{-24} kg\, {A} {m}/{s}$$

C
$$1.0 \times {10}^{24} kg \,{A} {m}/{s}$$

D
$$2.0 \times {10}^{24} kg\, {A} {m}/{s}$$

E
$$1.0 \times {10}^{44} kg \,{A} {m}/{s}$$

Solution

From de Broglie hypothesis , the linear momentum, $$p=\dfrac{h}{\lambda}=\dfrac{6.6\times 10^{-34}}{6.6\times 10^{-10}}=10^{-24} kg A^o m/s$$
Question 4
1 / -0

According to the Heisenberg uncertainty principle:

A

Position of electron can be found exactly if its momentum is known.

B

Momentum of an electron can be found exactly if its position is known.

C

The lowest energy of an atom can hold only one electron.

D

Light has a dual nature- wave and photon.

E
There is a limit to the accuracy of the measurement of subatomic particles.

Solution

According to the Heisenberg uncertainty principle, the position and the momentum of the particle cannot be measured accurately simultaneously. Thus there is a limitation to the accuracy of the measurement of subatomic particles.
Question 5
1 / -0

According to the theory of relativity, all laws of nature are the same in reference frames that:

A
accelerate

B
vibrate

C
rotate

D
Oscillate

E
move at a constant rate

Solution

According to the theory of relativity, the laws of nature are same in all inertial frames which are move with constant velocity. Thus, the option E will correct.
Question 6
1 / -0

Identify the reason why an observer cannot detect the wave nature of a fast moving truck .

A
The momentum of the truck is too large

B
The velocity of the wave is too large

C
There are no waves to be detected

D
The frequency is too low

E
The wavelengths are too small

Solution

The de-Broglie's wavelength associated with a moving matter is given by ,
$$\lambda=h/p$$ ,
where $$h=$$ planck's constant ,
$$p=$$ momentum of matter ,
now , a moving truck has a very small momentum therefore the wavelength associated with it is very large or frequency is very much low , so an observer cannot observe it .
Question 7
1 / -0

How do we know for sure that only one of the plots pictured as shown could be a correct graph representing the photoelectric effect for some metal ?

A
All graphs like this must have the same y-intercept

B
All graphs like this must have the same x-intercept

C
All graphs like this must have the same slope

D
All graphs like this must tilt downward

E
More than one of these graph could correctly represent the photoelectric effect

Solution

Using $$K.E_{max} = h\nu - \phi$$

Thus $$K.E_{max}$$ Vs $$\nu$$ graph for a certain metal has constant slope i.e $$ h $$. Hence all the graphs like this must have the same slope.Thus option C is correct.
Question 8
1 / -0

Which of the pictured graphs shows the metal with the greatest work function?

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

E
$$5$$

Solution

The photoelectric equation for light incident on metals is given by
$$h\nu=W_0+KE$$
$$\implies KE=h\nu-W_0$$
Therefore kinetic energy is lowest of same frequency for metal with highest work function.
Hence correct answer is option E.
Question 9
1 / -0

Relation between wavelength of photon and electron of same energy is

A
$$\lambda_{ph} > \lambda_e$$

B
$$\lambda_{ph} < \lambda_e$$

C
$$\lambda_{ph} = \lambda_e$$

D
$$\frac{\lambda_e}{\lambda_{ph}}=constant$$

Solution

For the same energy, the momentum of electron is more than that of photon $$\Rightarrow { p }_{ e }>{ p }_{ ph }$$
$${ \lambda }_{ e }=\dfrac { h }{ { p }_{ e } } \quad \quad and\quad \quad { \lambda }_{ ph }=\dfrac { h }{ { p }_{ ph } } \\ \Rightarrow { \lambda }_{ ph }>{ \lambda }_{ e }$$
Question 10
1 / -0

The pictured graph shows the relationship between the maximum kinetic energy of electrons flying off the surface of a metal versus the frequency of light striking the metal surface as part of the photoelectric effect.
According to this graph, what will happen when light of frequency $$7\times 10^{14}Hz$$ strikes the metal surface?

A
Electrons will be buried deeper within the surface

B
Electrons will be emitted with negative kinetic energy

C
A small number of electrons will be emitted with a small amounts of kinetic energy

D
No electrons will be emitted

E
The light will only knock loose electrons off the surface of the metal

Solution

From figure, the threshold frequency of the metal $$\nu_{th} = 10\times 10^{14}$$ Hz
When light of frequency greater than the threshold frequency of the metal falls on the surface of metal, only then the photoelectrons are emitted. As the light used has frequency less that the threshold frequency of the metal, thus no electrons are emitted.
Hence option D is correct.

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Dual Nature of Radiation and Matter Test - 20

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Dual Nature of Radiation and Matter Test - 20

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Question 1

electrons are too small to be studied.

every photon is exactly the same size.

the more you know about the momentum of an electron, the less you can know about its position.

the more you know about the energy of a photon, the less you can know about its frequency.

you cannot state with accuracy the number of electrons in atom.

Solution

Question 2

We cannot know for certain when any given radioactive particle will undergo decay

We cannot know both the momentum and the position of a particle at the same time

The laws of physics are the same in all intertial reference frames

Light exhibits both wave and particle properties

An unobserved particle can be in two places at the same time

Solution

Question 3

$$1.0 \times {10}^{-44} kg\, {A} {m}/{s}$$

$$1.0 \times {10}^{-24} kg\, {A} {m}/{s}$$

$$1.0 \times {10}^{24} kg \,{A} {m}/{s}$$

$$2.0 \times {10}^{24} kg\, {A} {m}/{s}$$

$$1.0 \times {10}^{44} kg \,{A} {m}/{s}$$

Solution

Question 4

Position of electron can be found exactly if its momentum is known.

Momentum of an electron can be found exactly if its position is known.

The lowest energy of an atom can hold only one electron.

Light has a dual nature- wave and photon.

There is a limit to the accuracy of the measurement of subatomic particles.

Solution

Question 5

accelerate

vibrate

rotate

Oscillate

move at a constant rate

Solution

Question 6

The momentum of the truck is too large

The velocity of the wave is too large

There are no waves to be detected

The frequency is too low

The wavelengths are too small

Solution

Question 7

All graphs like this must have the same y-intercept

All graphs like this must have the same x-intercept

All graphs like this must have the same slope

All graphs like this must tilt downward

More than one of these graph could correctly represent the photoelectric effect

Solution

Question 8

$$1$$

$$2$$

$$3$$

$$4$$

$$5$$

Solution

Question 9

$$\lambda_{ph} > \lambda_e$$

$$\lambda_{ph} < \lambda_e$$

$$\lambda_{ph} = \lambda_e$$

$$\frac{\lambda_e}{\lambda_{ph}}=constant$$

Solution

Question 10

Electrons will be buried deeper within the surface

Electrons will be emitted with negative kinetic energy

A small number of electrons will be emitted with a small amounts of kinetic energy

No electrons will be emitted

The light will only knock loose electrons off the surface of the metal

Solution

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