The wavelength of a neutron can be calculated using the de Broglie wavelength formula:

$\lambda = \frac{h}{mv}$

where:

• $\lambda$ is the wavelength,
• $h$ is Planck's constant $(6.626 \times 10^{-34} \, \text{J·s})$,
• $m$ is the mass of the neutron $(1.675 \times 10^{-24} \, \text{g})$,
• $v$ is the velocity of the neutron $(250 \, \text{cm/s})$.

Before proceeding, we need to convert all quantities to SI units:

• Mass: $1.675 \times 10^{-24} \, \text{g} = 1.675 \times 10^{-27} \, \text{kg}$,
• Velocity: $250 \, \text{cm/s} = 2.5 \, \text{m/s}$.

Now, let's calculate the wavelength:

$\lambda = \frac{6.626 \times 10^{-34} \, \text{J·s}}{(1.675 \times 10^{-27} \, \text{kg})(2.5 \, \text{m/s})}$

I'll compute this.The wavelength of the neutron is approximately 158.23 nm.

This matches the closest option of 160 nm.

Would you like more details or have any further questions? Here are 5 related questions to consider:

1. How does the mass of a particle affect its wavelength?
2. What is the significance of the de Broglie wavelength in quantum mechanics?
3. How does the velocity of a particle influence its wavelength?
4. What are some practical applications of neutron wavelengths in science?
5. How does the wavelength of a neutron compare to that of an electron?

Tip: Remember that heavier particles like neutrons have shorter wavelengths at the same velocity compared to lighter particles like electrons.