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Calculate the (a) Momentum (b) De Broglie wavelength of the electrons accelerated through a potential difference of 56 V.

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Question Calculate the (a) Momentum

(b) De Broglie wavelength of the electrons accelerated through a potential difference of 56 V.

Medium Open in App

Updated on : 2022-09-05

(a) Potential difference, V=56 volts

Solution Verified by Toppr

At equilibrium, Kinetic energy is accelerating potential.

2 mv 2 ​ =eV v=4.44×10 6 m/s P=mv ⇒9.1×10 −31 ×4.44×10 6 =4.04×10 −24

where m is the mass of the electron.

(b) De Broglie wavelength is given by

λ= V ​ 12.27×10 −10 ​ ⇒ 56 ​ 12.27×10 −10 ​ =0.164 nm Video Explanation

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A Calculate the momentum of the electrons accelerated through a potential difference of 56 V.B A Calculate the momentum of the electrons accelerated through a potential difference of 56 V.

A Calculate the momentum of the electrons accelerated through a potential difference of 56 V.B A Calculate the momentum of the electrons accelerated through a potential difference of 56 V.

Byju's Answer Standard XI Accountancy

Capabilities of Computer

A Calculate t... Question

A) Calculate the momentum of the electrons accelerated through a potential difference of 56 V.

B) A) Calculate the momentum of the electrons accelerated through a potential difference of 56 V.

Open in App Solution

A) Step 1: Find speed of each electron.

Formula used: E = 1 2 m v 2 = e V Given,

potential difference,

V = 56 V

At equilibrium, the kinetic energy of each electron with speed(v) is related to the accelerating potential(V) as,

E = 1 2 m v 2 = e V

Here, Mass of an electron,

m = 9.1 × 10 − 31 kg

Charge on an electron,

e = 1.6 × 10 − 19 C

Velocity of the electron

v = √ 2 e V m v = √ 2 × 1.6 × 10 − 19 × 56 9.1 × 10 − 31 = 4.44 × 10 6 m / s

Step 2: Find momentum of each electron.

Formula used : p = m v

The momentum of each accelerated electron,

p = mv p = 9.1 × 10 − 31 × 4.44 × 10 6 p = 4.04 × 10 − 24 kg m/s

Therefore, the momentum of each electron is

4.04 × 10 − 24 kg m/s Final answer: 4.04 × 10 − 24 kg m/s B) Formula used : λ = 12.27 √ v A

Given, accelerating potential difference,

V = 56 V

de Broglie wavelength of an electron accelerating through a potential V, is given by the relation:

λ = 12.27 √ v ∘ A λ = 12.27 √ 56 × 10 − 10 m λ = 0.164 nm

Therefore, the de Broglie wavelength of each electron is

0.164 nm . Final answer: 0.164 nm Suggest Corrections 4 Video Solution

NCERT - Grade 12 - Physics - Dual Nature of Radiation and Matter - Q12_02

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SIMILAR QUESTIONS

Q.

Calculate the (a) Momentum

(b) De Broglie wavelength of the electrons accelerated through a potential difference of 56 V.

Q.

Calculate the (a) momentum, and

(b) de Broglie wavelength of the electrons accelerated through a potential difference of 56 V.

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Q. A particle carrying 5 electrons starts from rest and is accelerated through a potential difference of 8900V. Calculate the K.E. acquired by it in MeV.

( C h a n g e o n e l e c t r o n = 1.6 × 10 − 19 C ) View More EXPLORE MORE

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Standard XI Accountancy

स्रोत : byjus.com

Calculate the momentum and de

Mass of electorn =m =9.1 xx 10^(-31)kg Potential difference= V=56V de-Broglie wavelength of electron =lamda =(h)/(sqrt(2meV)) =(6.62 xx 10^(-34))/(sqrt(2 xx 9.1 xx 10^(-31) xx 1.6 xx 10^(-19) xx 56)) =(6.62 xx 10^(-34))/(40.38 xx 10^(-25)) =0.1639 xx 10^(-9)m lamda= 1.639 xx 10^(-10) m= 1.639 Å Momentum of electron =P =(h)/(lamda) =(6.62 xx 10^(-34))/(1.639 xx 10^(-10)) P= 4.029 xx 10^(-24)kg m//s

Calculate the momentum and

de-Broglie wavelength of the electrons accelerated through a potential difference of 56V.

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Updated On: 27-06-2022

Text Solution Solution Mass of electorn = m = 9.1 × 10 − 31 k g

Potential difference= V=56V

de-Broglie wavelength of electron

= λ = h √ 2 m e V = 6.62 × 10 − 34 √ 2 × 9.1 × 10 − 31 × 1.6 × 10 − 19 × 56 = 6.62 × 10 − 34 40.38 × 10 − 25 = 0.1639 × 10 − 9 m λ = 1.639 × 10 − 10 m = 1.639 Å

Momentum of electron

= P = h λ = 6.62 × 10 − 34 1.639 × 10 − 10 P = 4.029 × 10 − 24 k g m / s Answer

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