Question

at a fixed velocity, which of the following will have the longest wavelength​

Answer 1

CORRECT QUESTION:

Moving at a fixed velocity, which of the following has longest De-Broglie wavelength?

• $\beta$ particle
• $\alpha$ particle
• proton
• neutron

Calculation:

General equation for De-Broglie wavelength is as follows:

$\rm \: \lambda = \dfrac{h}{mv}$

• 'h' is Planck's Constant, 'm' is mass and 'v' is Velocity.

For constant 'v', we can say:

$\rm \implies \lambda \propto \dfrac{1}{m}$

• Now, $\beta$ particle has the least mass (1/2000 amu), it has maximum wavelength.

Beta particles have max De-Broglie Wavelength.

Answer 2

Explanation:

The question statement is slightly incomplete as it does not give any options based on which we have to select.

However in general if we look at the De Broglie equation of wavelength we find that wavelength of any particle is inversely proportional to the mass of the particle given that velocity is constant. This means that the lesser the mass of the particle the longer will be its wavelength