The wavelength of light from the spectral emission line of sodium is 589nm. Find the kinetic energy at which (a) an electron and (b) a neutron would have the same deBroglie wavelength. Given that mass of neutron`=1.66xx10^(-27)kg`

Explanation

To solve the problem, we need to find the kinetic energy at which an electron and a neutron would have the same de Broglie wavelength of 589 nm. We will use the de Broglie wavelength formula and the kinetic energy formula to derive the required energies.

### Step-by-Step Solution:

1. **Given Data**:
- Wavelength, \( \lambda = 589 \, \text{nm} = 589 \times 10^{-9} \, \text{m} \)
- Mass of neutron, \( m_n = 1.66 \times 10^{-27} \, \text{kg} \)
- Mass of electron, \( m_e = 9.1 \times 10^{-31} \, \text{kg} \)
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