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PHXII11:DUAL NATURE OF RADIATION AND MATTER

357609 A photon of wavelength $4000 \overset{o}{A}$ is passing through vacuum. The effective mass and momentum of the photon are respectively

1

5 \times 10^{- 35} k g, 1.5 \times 10^{- 26} k g - m / s

2

5 \times 10^{- 36} k g, 1.5 \times 10^{- 27} k g - m / s

3

5 \times 10^{- 36} k g, 1.67 \times 10^{- 43} k g - m / s

4 Zero,

1.5 \times 10^{- 26} k g - m / s

Explanation:

$p = \frac{h}{λ} = \frac{6.6 \times 10^{- 34}}{4400 \times 10^{- 10}} = 1.5 \times 10^{- 27} k g - m / s$
and mass $m = \frac{p}{c} = \frac{1.5 \times 10^{- 27}}{3 \times 10^{8}} = 5 \times 10^{- 36} k g$

PHXII11:DUAL NATURE OF RADIATION AND MATTER

357610 Assertion :
The de Broglie equation has significance for any microscopic particle.
Reason :
The de Broglie wavelength is inversely proportional to the mass of the object if velocity is constant.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$λ = \frac{h}{m v}$ . Here $h$ indicates quantum or microscopic nature. $λ$ is appreciable only if $m$ is low. The de Broglie equation extends wave particle duality to all microscopic particles, predicting their associated wavelengths based on momentum. It plays a crucial role in explaining quantum effects, facilitating techno-logical applications in diffraction, interference, and high precision measurements. The deBroglie equation is a fundamental concept in quantum mechanics. So correct option is (1) .

PHXII11:DUAL NATURE OF RADIATION AND MATTER

357611 A wave is associated with matter when it is

1 Stationary

2 In motion with a velocity

3 In motion with speed of light

4 In motion with speed greater than that of light

PHXII11:DUAL NATURE OF RADIATION AND MATTER

357612 An electron and photon have same wavelength. If $E$ is the energy of photon and $P$ is the momentum of electron, then the magnitude of $\frac{E}{p}$ in $S I$ unit is

1

3.0 \times 10^{8}

2

3.33 \times 10^{- 9}

3

9 \times 10^{16}

4

1.1 \times 10^{- 19}

Explanation:

For electron, $p = \frac{h}{λ}$ ; and for photon, $E = \frac{h c}{λ}$
$∴ \frac{E}{p} = \frac{h c / λ}{h / λ} = c = 3 \times 10^{8} m s^{- 1}$

PHXII11:DUAL NATURE OF RADIATION AND MATTER

357609 A photon of wavelength $4000 \overset{o}{A}$ is passing through vacuum. The effective mass and momentum of the photon are respectively

1

5 \times 10^{- 35} k g, 1.5 \times 10^{- 26} k g - m / s

2

5 \times 10^{- 36} k g, 1.5 \times 10^{- 27} k g - m / s

3

5 \times 10^{- 36} k g, 1.67 \times 10^{- 43} k g - m / s

4 Zero,

1.5 \times 10^{- 26} k g - m / s

Explanation:

$p = \frac{h}{λ} = \frac{6.6 \times 10^{- 34}}{4400 \times 10^{- 10}} = 1.5 \times 10^{- 27} k g - m / s$
and mass $m = \frac{p}{c} = \frac{1.5 \times 10^{- 27}}{3 \times 10^{8}} = 5 \times 10^{- 36} k g$

PHXII11:DUAL NATURE OF RADIATION AND MATTER

357610 Assertion :
The de Broglie equation has significance for any microscopic particle.
Reason :
The de Broglie wavelength is inversely proportional to the mass of the object if velocity is constant.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$λ = \frac{h}{m v}$ . Here $h$ indicates quantum or microscopic nature. $λ$ is appreciable only if $m$ is low. The de Broglie equation extends wave particle duality to all microscopic particles, predicting their associated wavelengths based on momentum. It plays a crucial role in explaining quantum effects, facilitating techno-logical applications in diffraction, interference, and high precision measurements. The deBroglie equation is a fundamental concept in quantum mechanics. So correct option is (1) .

PHXII11:DUAL NATURE OF RADIATION AND MATTER

357611 A wave is associated with matter when it is

1 Stationary

2 In motion with a velocity

3 In motion with speed of light

4 In motion with speed greater than that of light

PHXII11:DUAL NATURE OF RADIATION AND MATTER

357612 An electron and photon have same wavelength. If $E$ is the energy of photon and $P$ is the momentum of electron, then the magnitude of $\frac{E}{p}$ in $S I$ unit is

1

3.0 \times 10^{8}

2

3.33 \times 10^{- 9}

3

9 \times 10^{16}

4

1.1 \times 10^{- 19}

Explanation:

For electron, $p = \frac{h}{λ}$ ; and for photon, $E = \frac{h c}{λ}$
$∴ \frac{E}{p} = \frac{h c / λ}{h / λ} = c = 3 \times 10^{8} m s^{- 1}$

PHXII11:DUAL NATURE OF RADIATION AND MATTER

357609 A photon of wavelength $4000 \overset{o}{A}$ is passing through vacuum. The effective mass and momentum of the photon are respectively

1

5 \times 10^{- 35} k g, 1.5 \times 10^{- 26} k g - m / s

2

5 \times 10^{- 36} k g, 1.5 \times 10^{- 27} k g - m / s

3

5 \times 10^{- 36} k g, 1.67 \times 10^{- 43} k g - m / s

4 Zero,

1.5 \times 10^{- 26} k g - m / s

Explanation:

$p = \frac{h}{λ} = \frac{6.6 \times 10^{- 34}}{4400 \times 10^{- 10}} = 1.5 \times 10^{- 27} k g - m / s$
and mass $m = \frac{p}{c} = \frac{1.5 \times 10^{- 27}}{3 \times 10^{8}} = 5 \times 10^{- 36} k g$

PHXII11:DUAL NATURE OF RADIATION AND MATTER

357610 Assertion :
The de Broglie equation has significance for any microscopic particle.
Reason :
The de Broglie wavelength is inversely proportional to the mass of the object if velocity is constant.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$λ = \frac{h}{m v}$ . Here $h$ indicates quantum or microscopic nature. $λ$ is appreciable only if $m$ is low. The de Broglie equation extends wave particle duality to all microscopic particles, predicting their associated wavelengths based on momentum. It plays a crucial role in explaining quantum effects, facilitating techno-logical applications in diffraction, interference, and high precision measurements. The deBroglie equation is a fundamental concept in quantum mechanics. So correct option is (1) .

PHXII11:DUAL NATURE OF RADIATION AND MATTER

357611 A wave is associated with matter when it is

1 Stationary

2 In motion with a velocity

3 In motion with speed of light

4 In motion with speed greater than that of light

PHXII11:DUAL NATURE OF RADIATION AND MATTER

357612 An electron and photon have same wavelength. If $E$ is the energy of photon and $P$ is the momentum of electron, then the magnitude of $\frac{E}{p}$ in $S I$ unit is

1

3.0 \times 10^{8}

2

3.33 \times 10^{- 9}

3

9 \times 10^{16}

4

1.1 \times 10^{- 19}

Explanation:

For electron, $p = \frac{h}{λ}$ ; and for photon, $E = \frac{h c}{λ}$
$∴ \frac{E}{p} = \frac{h c / λ}{h / λ} = c = 3 \times 10^{8} m s^{- 1}$

PHXII11:DUAL NATURE OF RADIATION AND MATTER

357609 A photon of wavelength $4000 \overset{o}{A}$ is passing through vacuum. The effective mass and momentum of the photon are respectively

1

5 \times 10^{- 35} k g, 1.5 \times 10^{- 26} k g - m / s

2

5 \times 10^{- 36} k g, 1.5 \times 10^{- 27} k g - m / s

3

5 \times 10^{- 36} k g, 1.67 \times 10^{- 43} k g - m / s

4 Zero,

1.5 \times 10^{- 26} k g - m / s

Explanation:

$p = \frac{h}{λ} = \frac{6.6 \times 10^{- 34}}{4400 \times 10^{- 10}} = 1.5 \times 10^{- 27} k g - m / s$
and mass $m = \frac{p}{c} = \frac{1.5 \times 10^{- 27}}{3 \times 10^{8}} = 5 \times 10^{- 36} k g$

PHXII11:DUAL NATURE OF RADIATION AND MATTER

357610 Assertion :
The de Broglie equation has significance for any microscopic particle.
Reason :
The de Broglie wavelength is inversely proportional to the mass of the object if velocity is constant.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$λ = \frac{h}{m v}$ . Here $h$ indicates quantum or microscopic nature. $λ$ is appreciable only if $m$ is low. The de Broglie equation extends wave particle duality to all microscopic particles, predicting their associated wavelengths based on momentum. It plays a crucial role in explaining quantum effects, facilitating techno-logical applications in diffraction, interference, and high precision measurements. The deBroglie equation is a fundamental concept in quantum mechanics. So correct option is (1) .

PHXII11:DUAL NATURE OF RADIATION AND MATTER

357611 A wave is associated with matter when it is

1 Stationary

2 In motion with a velocity

3 In motion with speed of light

4 In motion with speed greater than that of light

PHXII11:DUAL NATURE OF RADIATION AND MATTER

357612 An electron and photon have same wavelength. If $E$ is the energy of photon and $P$ is the momentum of electron, then the magnitude of $\frac{E}{p}$ in $S I$ unit is

1

3.0 \times 10^{8}

2

3.33 \times 10^{- 9}

3

9 \times 10^{16}

4

1.1 \times 10^{- 19}

Explanation:

For electron, $p = \frac{h}{λ}$ ; and for photon, $E = \frac{h c}{λ}$
$∴ \frac{E}{p} = \frac{h c / λ}{h / λ} = c = 3 \times 10^{8} m s^{- 1}$