Question

If the potential difference used to accelerate electrons is tripled, by what factor does the de-Broglie wavelength associated with electrons change?

Options

• wavelength is decreased to `1/3` times.

• wavelength is decreased to `1/sqrt 3` times.

• wavelength is decreased to `1/9` times.

• wavelength is decreased to `1/18` times.

Answer 1

Wavelength is decreased to `bb(1/sqrt 3)` times.

Explanation:

Given: V₂ = 3V₁

For an electron accelerated through a potential V,

λ ∝ `1/sqrt V`

∴ `lambda_2/lambda_1 = sqrt (V_1/V_2)`

⇒ λ₂ = `lambda_1 xx sqrt (V_1/(3 V_1))`

= `lambda_1/sqrt 3`