Calculate the wavelength of a neutron that has a velocity of 250 cm/s.

mneutron = 1.675 × 10–24 g

Question 11 options:

1.6 pm


0.016 nm


1.6 × 10–4 nm


160 nm


0.16 nm

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.

Calculate the wavelength of a neutron that has a velocity of 250 cm/s. mneutron = 1.675 × 10–24 g

Learn how to calculate the de Broglie wavelength of a neutron with a velocity of 250 cm/s and mass of 1.675 × 10–24 g. The solution involves converting units to SI, applying the de Broglie equation, and understanding the quantum mechanical concepts of wave-particle duality.

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