Question

Bakra there exist a relation between wavelength and potential difference can you drive that relation​

Answer 1

Answer:

Explanation:

An electron that is accelerated from rest through an electric potential difference of V has a de Broglie wavelength of λ. Investigate the relationship between V and λ." I had two arguments that led to two significantly distinct results.

The first argument: λ∝1V. From the Planck relation, we have:

E=hf=hcλ

But after acceleration through the electric potential difference, the energy of the electron is eV, where e is the charge of the electron. As such,

eV=hcλ

λ=hce⋅1V

⟹λ∝1V

The second argument: λ∝1V√. From de Brogile's equation, we have

p=hλ

mv=hλ

m2v2=h2λ2

m2v22m=h22mλ2

12mv2=h22m⋅1λ2

But since the kinetic energy of the electron is equal to the energy gained from accelerating through the electric potential,

eV=h22m⋅1λ2

λ2=h22meV

λ=h2me−−−−√⋅1V−−√

⟹λ∝1V−−√