Question

an electron ,an alpha particle and a proton have the same kinetic energy.which of these particles has the shortest de broglie wavelength? ​

Answer 1

An electron, an alpha particle, and a proton have the same kinetic energy. ... De broglie wavelength lambda=h/mv, where m is the mass of the particle. More the mass, lesss the wavelength. The alpha particle has the highest mass, so it has the shortest wavelength

Answer 2

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The alpha particle has the shortest wavelength.

Explanation:

Given:  

An electron, an alpha particle, and a proton has the same kinetic energy.

The mass of the electron  m e  =  9.1  ×  10 ^− 31  kg

The mass of the proton  m p  =  1.67  ×  10 ^− 27  kg

The mass of the alpha particle  m α  =  4  ×  m p  =  6.68  ×  10^ − 27  kg  

Now recall that the De Broglie wavelength is computed as:

⇒  λ  =  h  / √ 2 m K

The particles have the same kinetic energy So:

⇒  λ  ∝  1  /√ m

The wavelength is inversely proportional to the square root of the mass. Thus the particle with higher mass has the shortest wavelength.  

In this case, protons are heavier compared to electrons, and alpha particles are composed of two protons. Hence the alpha particle is the heaviest compared to a proton and an electron.

Hope this will help you..✌✌