COMEDK 2024 Shift 1 Paper

To solve this problem, let's start by understanding the relationship between the kinetic energy, mass, and de Broglie wavelength of the particles.
The de Broglie wavelength λ of a particle is given by:
λ=‌

h

p

where h is Planck's constant and p is the momentum of the particle.
The momentum p can be expressed as:
p=√2mK

where m is the mass and K is the kinetic energy of the particle.
Let's denote the masses and kinetic energies of particles A and B as follows:
Mass of particle A:mA
Mass of particle B: mB
Since the mass of particle A is double that of particle B :
mA=2mB

Kinetic energy of particle A: KA
Kinetic energy of particle B: KB
Given that the kinetic energy of particle B is ‌

1

8

th that of A :
KB=‌

KA

8

Now, let's find the ratio of the de Broglie wavelengths of particles A and B. The de Broglie wavelength for particle A is:
λA=‌

h

√2mAKA

The de Broglie wavelength for particle B is:
λB=‌

h

√2mBKB

We need to find the ratio ‌

λA

λB

:
Substitute the given values:
Thus, the ratio of the de Broglie wavelength of A to that of B is:
Option C: 1:4