Question

a proton and an alpha particle are accelerated through the same potential difference.which one of the tow has (1) greater de- Broglie wavelength,and (2) less kinetic energy? justify your answer.

Answer 1

The proton should have more de Broglie wavelength due to lesser mass.

2. the alpha particle has more KE due to lesser wavelength..

use the de broglie wavelength formula & also E=hc/(wavelength)

Answer 2

The mass of a proton =1 u.
The mass of an alpha particle =4u.
The charge of a proton =+1.
The charge of an alpha particle =+2.

1) de broglie wavelength =
$\frac{h}{ \sqrt{2mqv} }$

where, h= Planck's constant, m=mass, v= potential, q=charge.
So, comparing with the masses and charges, proton will have a greater de - broglie wavelength.

2)Kinetic energy = hc/λ
where, h=Planck's constant, c=speed of light, λ = de broglie wavelength.
So, comparing from the wavelengths, the Kinetic energy of proton will be lesser than that of the alpha particle.