Question

A proton is moving at a speed of 5.0 × 10⁴ m/s. The de Broglie wavelength associated with it is _____.

(m_p = 1.67 × 10^-27 kg, h = 6.63 × 10^-34 J s)

1. 0.38 × 10^-11 m
2. 0.79 × 10^-11 m
3. 1.20 × 10^-11 m
4. 1.58 × 10^-11 m

Answer 1

Correct Answer - Option 2 : 0.79 × 10^-11 m

Concept:

De Broglie wavelength:  All particles could be treated as matter waves with a wavelength.

Frequency is given by the following equation:

\(λ = \frac{h}{mv}\)

Where λ is de Broglie wavelength, h is Planck's const, m is mass, v is the velocity.

When an electron is accelerated its de Broglie wavelength is given by

\(λ = \frac{\sqrt{150}}{\sqrt V} A\)

Where V is the potential difference in which electron is accelerated.

Calculation:

Given that, v = 5 × 10⁴, mp = 1.67 × 10-27 kg, h = 6.63 × 10-34 J s

Frequency is given by,

\(λ = \frac{h}{mv}\) = \(\frac{6.63×10^{-34}}{1.67× 10^{-27}×5×10^{4}}=0.79×10^{-11}\)

The de Broglie wavelength associated with it is 0.79 × 10^-11m.