Question

Q.The light from a highway sodium lamp has wavelength 589 nm. What is energy in ev of photon emitted form lamp?

Answer 1

Question #58596, Physics / Quantum Mechanics

The light from a highway sodium lamp has wavelength 589 nm. What is energy in ev of photon emitted from lamp?

Solution:

$$\lambda = 589 \, \text{nm} = 5,89 \cdot 10^{-7} \, \text{m};$$

It is known that the energy photon is determined from the equation

$$E = h\nu, \text{ where } \nu = \frac{c}{\lambda}.$$ $$h = 4.135667662(25) \times 10^{-15} \, \text{eV} \cdot \text{s} \approx 4.14 \cdot 10^{-15} \, \text{eV} \cdot \text{s} - \text{Planck constant and}$$ $$c = 299\,792\,458 \, \text{m/s} \approx 3 \cdot 10^{8} \, \text{m/s} - \text{Speed of light}.$$

Energy of photon in eV:

$$E = h \frac{c}{\lambda} = 4.14 \cdot 10^{-15} \, [\text{eV} \cdot \text{s}] \cdot 3 \cdot \frac{3 \cdot 10^{8} \, [\text{m/s}]}{5.89 \cdot 10^{-7} \, [\text{m}]} = 2.1 \, \text{eV}$$

Answer: $E = h \frac{c}{\lambda} = 2.1 \, \text{eV}$

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