Final answer:
The de Broglie wavelength of a neutron is halved when its kinetic energy is quadrupled, so when the kinetic energy is 4K, the wavelength will be λ/2. Option number b is correct.
Step-by-step explanation:
The question revolves around the concept of the de Broglie wavelength of a particle in quantum mechanics. According to de Broglie's hypothesis, the wavelength (λ) of a particle is inversely proportional to its momentum (p), which can be related to kinetic energy (K).
The de Broglie wavelength is given by λ = h/p, where h is Planck's constant. When kinetic energy is quadrupled (from K to 4K), the speed of the particle, and hence its momentum, increases by a factor of two because kinetic energy is proportional to the square of the velocity. Consequently, the de Broglie wavelength becomes half of its original value.
The answer to the question "What will be its wavelength when its kinetic energy is 4K?" is therefore λ/2, meaning the wavelength is halved when the kinetic energy is quadrupled.