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Dual Nature of Radiation and Matter

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Dual Nature of Radiation and Matter Class 12th

The de Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100V. What should be the ratio of their wavelengths? (m? = 1.00727u, m? = 0.00055u)

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alok kumar singh

Contributor-Level 10

Using de-Broglie equation:
λ = h/p = h/√ (2mK) = h/√ (2meV)
λ ∝ 1/√m
λ? /λ? = √ (m? /m? ) = √ (1.00727/0.00055) = √1831 ≈ 43:1

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Dual Nature of Radiation and Matter Class 12th

A light beam of wavelength 500 nm is incident on a metal having work function of 1.25 eV, placed in a magnetic field of intensity B. The electrons emitted perpendicular to the magnetic field B, with maximum kinetic energy are bent into circular arc of radius 30cm. The value of B is __________ x x 10⁻⁷ T
Given hc = 20 * 10?²? J-m, mass of electron = 9 * 10⁻³¹ kg

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alok kumar singh

Contributor-Level 10

K = hc/λ - W?
K = (20*10? ²? )/ (500*10? ) - 1.25 * 1.6*10? ¹?
K = 4*10? ¹? - 2*10? ¹? = 2*10? ¹? J
R = √ (2mK)/ (eB)
B = √ (2mK)/ (eR) = √ (2 * 9*10? ³¹ * 2*10? ¹? ) / (1.6*10? ¹? * 30*10? ²)
B = √ (36*10? ) / (48*10? ²¹) = (6*10? ²? ) / (4.8*10? ²? ) = 1.25 * 10? T
B = 125 * 10? T

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a year ago

Dual Nature of Radiation and Matter Class 12th

A particle of mass 9.1 * 10?³¹ kg travels in a medium with a speed of 10? m/s and a photon of a radiation of linear momentum 10?²? kg m/s travels in vacuum. The wavelength of photon is _______ times the wavelength of the particle.

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Vishal Baghel

Contributor-Level 10

For photon, λ? = h/p = 6.6*10? ³? /10? ²? = 6.6*10? m
For a particle, λ? = h/mv = 6.6*10? ³? / (9.1*10? ³¹ * 10? ) ≈ 7.25*10? ¹? m
λ? /λ? = 6.6*10? / 7.25*10? ¹? ≈ 910

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a year ago

Dual Nature of Radiation and Matter Class 12th

A particle of mass 4M at rest disintegrates into two particles of mass M and 3M respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass M to that of mass 3M will be :

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Raj Pandey

Contributor-Level 9

MV? = 3MV? = p
λ = h/mv = h/p
λ? /λ? = 1

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Dual Nature of Radiation and Matter Class 12th

When radiation of wavelength λ is incident on a metallic surface, the stopping potential of ejected photoelectrons is 4.8 V. If the same surface is illuminated by radiation of double the previous wavelength, then the stopping potential becomes 1.6 V. The threshold wavelength of the metal is:

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alok kumar singh

Contributor-Level 10

By Einstein's equation of photoelectric effect,
hc/λ = hc/λ? + eVs
Now hc/λ = hc/λ? + e*4.8 . (i)
hc/ (2λ) = hc/λ? + e*1.6 . (ii)
Multiply (ii) by 2:
hc/λ = 2hc/λ? + e*3.2 . (iii)
Equating (i) and (iii):
hc/λ? + 4.8e = 2hc/λ? + 3.2e
1.6e = hc/λ?
Substitute this into (i)
hc/λ = 1.6e + 4.8e = 6.4e
Substitute this into (ii)
(6.4e)/2 = hc/λ? + 1.6e
3.2e = hc/λ? + 1.6e
1.6e = hc/λ?
From (i): hc/λ = hc/λ? + 3 (hc/λ? ) = 4hc/λ?
λ? = 4λ

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a year ago

Dual Nature of Radiation and Matter Class 12th

An electron moving with speed v and a photon moving with speed c, have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is :

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alok kumar singh

Contributor-Level 10

For electron,
λe = h/p ⇒ (KE)e = ½mv² = p²/ (2m) = (h²/λ²)/ (2m)
For photon,
λp = h/p ⇒ (K.E.)p = pc = hc/λ
KEe / KEp = (h²/ (2mλ²) / (hc/λ) = h/ (2mcλ)
But for electron p = mv = h/λ so h/λ = mv
KEe / KEp = mv / (2mc) = v/2c

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a year ago

Dual Nature of Radiation and Matter Class 12th

What should be the order of arrangement of de-Broglie wavelength of electron (λ?), an α – particle (λα) and proton (λ?) given that all have the same kinetic energy ?

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Raj Pandey

Contributor-Level 9

λ = h/mv = h/√2mK
For same K:
λ ∝ 1/√m
λ? : λ? : λ? = 1/√m? : 1/√m? : 1/√4m?
As m? > m? ,
λ? > λ? > λ?

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a year ago

Dual Nature of Radiation and Matter Class 12th

Given below are two statements:

Statements I : Two photons having equal linear momenta having equal waelengths

Statements II : If the wavelength of photon is decreases, then the momentum and energy of a photon will also decrease.

In the light of the above statements, choose the correct answer from the options given below.

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alok kumar singh

Contributor-Level 10

$p = \frac{h}{λ}$

So, two photons having equal linear momenta have equal wavelength. As wavelength decreases, momentum and energy of photon increases.

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a year ago

Dual Nature of Radiation and Matter Class 12th

Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is x : y. The value of x is………

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Vishal Baghel

Contributor-Level 10

Case I :- $2 ? - ? = \frac{1}{2} m v_{1}^{2} . . . . . . . . (i)$ $\frac{}{}_{}^{}$

Case II :- $10 ? - ? = \frac{1}{2} m v_{2}^{2} . . . . . . . . (i i)$ $\frac{}{}_{}^{}$

$\Rightarrow \frac{1}{9} = \frac{v_{1}^{2}}{v_{2}^{2}}$

$\Rightarrow v_{1} : v_{2} = 1 : 3$

x = 1

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New answer posted

a year ago

Dual Nature of Radiation and Matter Class 12th

The de Broglie wavelength of a proton and a - particle are equal. The ratio of their velocities is:

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Vishal Baghel

Contributor-Level 10

$λ = \frac{h}{p} o r λ = \frac{h}{m v}$

$λ_{p} = λ_{α} [G i v e n]$

$\frac{h}{m_{p} V_{p}} = \frac{h}{m_{α} v_{α}} \Rightarrow \frac{v_{p}}{v_{α}} = \frac{m_{α}}{m_{p}}$

$\Rightarrow \frac{v_{p}}{v_{α}} = \frac{4 m}{m} = \frac{4}{1}$ 0r 4: 1

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