Question

A proton and an electron have equal speeds. Find the ratio of de Broglie
wavelengths associated with them.
​

Answer 1

Explanation:

y=h/wv

yp/ye=h/wpv

/

h/eev

=we/mp

Ratio of wave length=we/wp

9.10×10

/

1.67×10

ratio=yp/ye

9.1×10 to the power of -4/1.67

Answer 2

Concept:

De Broglie wavelength can be defined as a wavelength that is associated with an object in relation to its momentum and mass. It can be defined as λ=h/mv.

Given:

A proton and the electron both are having the same speed.

Find:

The ratio of de-Broglie wavelengths which are associated with them.

Solution:

De Broglie wavelength is λ=h/mv, where h is Planck's constant, m is mass and velocity of the object.

The wavelength for electron,  λ₁ = h/m₁v₁

The wavelength for proton,  λ₂ = h/m₂v₂

and, v₁ = v₂

Taking the ratio of the wavelengths,

λ₁ : λ₂ = h/m₁v₁ : h/m₂v₂

Canceling the common terms,

λ₁ : λ₂ = m₂ : m₁

λ₁ : λ₂ = (1.67262192 × 10⁻²⁷) kg / (9.1093837 × 10⁻³¹) kg

λ₁ : λ₂ = 1836 : 1

Hence, the ratio of de-Broglie wavelengths which are associated with them is 1836: 1.

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