# the wavelength associated with material particles in motion are called

### Mohammed

Guys, does anyone know the answer?

get the wavelength associated with material particles in motion are called from screen.

## The wavelength associated with material particles in motion are called:..

Solution For The wavelength associated with material particles in motion are called:

Home CBSE Class 12 Physics Electrostats

**Question**

Question asked by Filo student

## The wavelength associated with material particles in motion are called:

Matter waves Seismic waves. Radio waves Microwaves.

Viewed by: **6,370** students

Updated on: Jan 10, 2023

## Solutions

(3)The wavelength associated with material particles in motion are called "de Broglie Wavelengths." The concept was introduced by French physicist Louis de Broglie in 1924. He proposed that all matter, including particles, have wave-like properties and are associated with a wavelength proportional to their momentum. This idea formed the basis of wave-particle duality, which states that particles can exhibit both wave-like and particle-like behavior, depending on the context. De Broglie's theory was later confirmed experimentally and is now considered a fundamental principle of quantum mechanics.

## 2 students asked the same question on Filo

Learn from their 1-to-1 discussion with Filo tutors.

8 mins

Uploaded on: 1/10/2023

Taught by Ved Parkash

Connect instantly with this tutor

Connect now

Total classes on Filo by this tutor - 3213

Teaches : Physics

Notes from this class (3 pages)

Download 86 0 Share

10 mins

Uploaded on: 1/10/2023

Taught by Debabrata Pradhan

Connect instantly with this tutor

Connect now

Total classes on Filo by this tutor - 1338

Teaches : Physics 107 0 Share

Connect with 50,000+ expert tutors in 60 seconds, 24X7

### Ask a tutor

### Practice more questions on Electrostats

**Question 1**

Medium Views: 5,751

Ten positively-charged particles are kept fixed on the x-axis at points x = 10 cm, 20 cm, 30 cm, ...., 100 cm. the first particle has a charge 1.0×10

−8 C , the second 8×10 −8 C , the third 27×10 −8

C and so on. The tenth particle has a charge 1000×10

−8

C. Find the magnitude of the electric force acting on a 1 C charge placed at the origin.

Book:

Concepts of Physics (HC Verma Part II)

View solution

**Question 2**

Easy Views: 5,213

The resistance of the filament of an electric bulb changes with temperature. If an electric bulb rated 220 volt and 100 watt is connected (220×.8) volt sources, then the actual power would be.

100×0.8watt 100×(0.8) 2 watt

Between 100×0.8 watt and 100 watt

Between 100×(0.8) 2

watt and 100×0.8 watt

View solution

**Question 3**

Medium Views: 5,718

Two coils A and B are mounted co-axially some distance apart. Coil A is given a current that changes sinusoidally with time. A current gets induced in coil B. How does the magnitude of current in coil B change if a metal plate is placed between the two coils.

Book:

Problems in Physics II for IIT JEE (McGraw Hill)

View solution

**Question 4**

Hard Views: 5,827

In the Figure FE is a man of height H standing on a floor. E is eye of the man and F is his foot. The distance between eye and the head is negligible. A steel ball of radius r is suspended in front of him. The distance of the ball from the man is H and height of the centre of the ball from the floor is

2 H

. It is given that r<∠. The surface of the ball acts like a mirror and the man sees his image in it. Calculate the angle subtended by the image at the eye of the man.

Book:

Problems in Physics II for IIT JEE (McGraw Hill)

View solution View more

### Students who ask this question also asked

**Question 1**

Views: 5,634

PARAGRAPH FOR QUESTIONS 56 - 57 A capacitor having a capacitance of 100jF is charged to a potential difference of 24 V. The charging battery is disconnected and the capacitor is connected to another battery of 12 V, with the positive plate of the capacitor joined with the positive terminal of the battery. 56. The charge flown through the 12 V battery is:

−600μC −1200μC 600μC 1800μC View 2 solutions

**Question 2**

Views: 5,968

capacitance of each capacitor is 3uF, the equivalent capacitance of A and B will be-

4 3 μF

3uF(c)6uF (d) 5 F43. The

View solution

**Question 3**

Views: 5,575

the smaller charge where the intensity is zero. 2. A charged particle of mass 2 mili gram remains freely in air in an electric field of strength 4 N/C directed upward. Calculate the charge and determine its nature (g=10 m/s

## de Broglie Wavelength

de Broglie wavelength is an important concept while studying quantum mechanics. The wavelength (λ) that is associated with an object in relation to its momentum and mass is known as de Broglie wavelength.

JEEIIT JEE Study MaterialDe Broglie Wavelength

## de Broglie Wavelength

de Broglie wavelength is an important concept while studying quantum mechanics. The wavelength (λ) that is associated with an object in relation to its momentum and mass is known as de Broglie wavelength. A particle’s de Broglie wavelength is usually inversely proportional to its force.

## de Broglie Waves

It is said that matter has a dual nature of wave-particles. de Broglie waves, named after the discoverer Louis de Broglie, is the property of a material object that varies in time or space while behaving similar to waves. It is also called matter-waves. It holds great similarity to the dual nature of light which behaves as particle and wave, which has been proven experimentally.

**Also Read:**Photoelectric Effect

The physicist Louis de Broglie suggested that particles might have both wave properties and particle properties. The wave nature of electrons was also detected experimentally to substantiate the suggestion of Louis de Broglie.

The objects which we see in day-to-day life have wavelengths which are very small and invisible, hence, we do not experience them as waves. However, de Broglie wavelengths are quite visible in the case of subatomic particles.

## de Broglie Wavelength for Electrons

In the case of electrons going in circles around the nuclei in atoms, the de Broglie waves exist as a closed-loop, such that they can exist only as standing waves, and fit evenly around the loop. Because of this requirement, the electrons in atoms circle the nucleus in particular configurations, or states, which are called stationary orbits.

## de Broglie Wavelength Formula and Derivation

de Broglie reasoned that matter also can show wave-particle duality, just like light, since light can behave both as a wave (it can be diffracted and it has a wavelength) and as a particle (it contains packets of energy hν). And also reasoned that matter would follow the same equation for wavelength as light namely,

**λ = h / p**

Where p is the linear momentum, as shown by Einstein.

### Derivation

de Broglie derived the above relationship as follows:

1) E = hν for a photon and λν = c for an electromagnetic wave.

2) E = mc2, means λ = h/mc, which is equivalent to λ = h/p.

Note: m is the relativistic mass, and not the rest mass; since the rest mass of a photon is zero.

Now, if a particle is moving with a velocity v, the momentum p = mv and hence λ = h / mv

Therefore, the de Broglie wavelength formula is expressed as;

**λ = h / mv**

## Applications of de Broglie Waves

1. The wave properties of matter are only observable for very small objects, de Broglie wavelength of a double-slit interference pattern is produced by using electrons as the source. 10 eV electrons (which is the typical energy of an electron in an electron microscope): de Broglie wavelength = 3.9 x 10-10 m.

This is comparable to the spacing between atoms. Therefore, a crystal acts as a diffraction grating for electrons. The diffraction pattern allows the crystal structure to be determined.

2. In a microscope, the size of the smallest features we can see is limited by the wavelength used. With visible light, the smallest wavelength is 400 nm = 4 x 10-7 m. Typical electron microscopes use wavelengths 1000 times smaller and can be used to study very fine details.

## Thermal de Broglie Wavelength

The thermal de Broglie wavelength (λth) is approximately the average de Broglie wavelength of the gas particles in an ideal gas at the specified temperature.

The thermal de Broglie wavelength is given by the expression:

λD = h / √ 2 π m kBT

where,

h = Planck constant,

m = mass of a gas particle,

kB = Boltzmann constant,

T = temperature of the gas,

λD = λth = thermal de Broglie wavelength of the gas particles.

**Also Read:**

Value of Planck’s Constant

Boltzmann Constant

## Bohr’s model for Hydrogen

The electrons move in circular orbits around the nucleus in atoms. The electrons have the form of disk-shaped clouds. In the hydrogen atom, the electron in the ground state with the minimum energy can be modelled by a rotating disk, the inner edge of which has the radius ½ rB(1) and the outer edge has the radius 3/2 rB (2) where rB is the Bohr radius.

If we assume that the electron’s orbit in the atom includes ‘n’ of de Broglie wavelengths, then in case of a circular orbit with the radius, for the circle perimeter and the angular momentum L of the electron we will obtain the following:

2 πr = n λB, L = rp = nh / 2π λB = h / p

This is exactly the postulate of the Bohr’s model for the Hydrogen atom. According to postulate, the angular momentum of the hydrogen atom is quantized and proportional to the number of the orbit ‘n’ and the Planck constant.

## Solved Problems

**Question 1: An electron and a photon have the same wavelength. If p is the momentum of the electron and E is the energy of the photon. The magnitude of p/E in S.I unit is**

**(a) 3.0108 (b) 3.3310-9**

**(c) 9.110-31 (d) 6.6410-34**

Answer: b

As we know that, for electron, λ = h/p

Or p = h/λ

And for photon E = hc / λ

Thus, p / E = 1 / c = 1 / (3 x 108 m/s) = 0. 33 x 10-8 s/m

**Question 2: What is the energy and wavelength of a thermal neutron?**

## The de

Click here👆to get an answer to your question ✍️ The de - Broglie wavelength associated with a material particle is :

Question

## The de-Broglie wavelength associated with a material particle is :

**A**

## directly proportional to its energy

**B**

## directly proportional to momentum

**C**

## inversely proportional to its energy

**D**

## inversely proportional to momentum

Medium Open in App

Updated on : 2022-09-05

Solution Verified by Toppr

Correct option is D)

The de Broglie wavelength is the wavelength λ, associated with a massive particle and is inversely proportional to its momentum, p.∴λ α p 1 i.e λ= p h where, h= planck's cnstant

Solve any question of Structure of Atom with:-

Patterns of problems

>

Was this answer helpful?

33 3

Guys, does anyone know the answer?