De Broglie Wavelength Calculator

The following are the steps on finding the de Broglie wavelength of a photon easily. Go through these guidelines and follow them to obtain the result.

• Get the energy of the photon particle.
• Multiply the speed of light with the planck's constant.
• Divide the result by the photon energy to check de Broglie Wavelength of photon.

de Broglie wavelength is defined as the wavelength in which the object is associated with its momentum and mass. The de Broglie wavelength and object force are inversely proportional to each other. This de Broglie wavelength equation shows the relationship between the nature of the particle and the nature of the body.

de Broglie Wavelength formula is λ = h/mv or λ = h/p

Where,

λ is de Broglie wavelength

m is the mass

v is the velocity

p is momentum

h is planck's constant i.e 6.62607015 x 10^-34 Js

De Broglie waves tells about the nature of the wave related to the particle.

According to Einstein, momentum of a photon p = mc --- (i)

Energy of the photon is E = mc² and E = hλ

hλ = mc²

m = hλ/c² --- (ii)

Substitute (ii) in (i)

p = (hλ/c²) * c

p = h/λ

λ = h/p

λ = h/mv

de Broglie Wavelength Example:

Question: Find the wavelength of the electron moving with a speed of 3 x 10⁶ m/s?

Answer:

Given that,

Velocity of the electron v = 3 x 10⁶ m/s

Mass of electron m = 9.1 x 10^-31 kg

Plank's constant h = 6.62607015 x 10^-34 Js

de-Broglie wavelength λ = h/mv

λ = 6.62607015 x 10^-34/(9.1 x 10^-31 * 3 x 10⁶)

= 6.62607015 x 10^-34/(27.3 x 10^-25)

= 24.27 x 10⁷ m

Therefore, de Broglie wavelength of an electron is 24.27 x 10⁷ m

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The de Broglie wavelength of an electron travelling at 1% of the speed of light. Let us find the details of the electron.

• Mass of the electron is 1 me or 9.10938356 x 10^-31 kg.
• Speed of the electron is 2,997,924.58 m/s
• Multiply the electron velocity and mass to check the momentum. p = mV = 2.7309245 x 10^-24 kg m/s
• Dividing the Planck's constant by the momentum to get the wavelength. h/p = 6.6261 x 10^-34/2.7309245 x 10^-24 = 2.426 x 10^-10 m.
• The de Broglie wavelength of the electron is equal to 0.24 nm.

The mass of the photon during the rest position is zero. The momentum of the photon is used to calculate the de Broglie wavelength of the photon.

1. Momentum of a photon is 6.8 x 10^-35 kg m/s
2. Divide Planck's constant by the momentum. h/p = 6.6261 x 10^-34/6.8 x 10^-35 = 9.74 m

The de Broglie wavelength of the photon is 9.74 m.

1. What is the de Broglie Wavelength equation?

de Broglie wavelength formula is λ = h/mv or λ = h/p.

2. What is the unit of de Broglie wavelength?

The unit of De Broglie wavelength meters.

3. How to calculate the de Broglie wavelength?

Obtain the energy of the photon from the question. Multiply Plack's constant with the velocity of light. Divide the product by the photon energy to check the de Broglie Wavelength.

4. What is de Broglie's principle?

de Broglie principle tells about the duality behaviour of matter. It says that matter can act as waves like light can act as waves and photons. The de Broglie equation relates the momentum of a particle to its wavelength that corresponds to the matter acting as a wave.