Question

# Calculate the energies of photons related to the two lines using the relationships expressed in the following equations. $E_{\text {photon }}=h v ; c=\lambda v ; E=h c / \lambda$

Solution

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Sodium’s two bright lines have wavelengths of 588.9590 nm and 589.9524 nm, and in order to find their energy we need to use the given relationships expressed in the following equations:

$E_{photon} = h\times \nu , c= \lambda \times \nu \Rightarrow E_{photon}=\dfrac{h\times c}{\lambda}$

Notes:

588.9590 nm $\Rightarrow 588.9590\cdot10^{-9} \ \text{m} , 589.9524 nm \Rightarrow 589.9524\cdot10^{-9} \ \text{m}$

h: Plank's constant , c: speed of light in vacuum.

First line: $E_{photon} =\dfrac{3.00\cdot10^8 \ \text{m.s}^{-1} \times 6.626\cdot10^{-34} \ \text{J.s}}{588.9590\cdot10^{-9} \ \text{m}} =3.38\cdot10^{-19} \ \text{J}$

Second line: $E_{photon} =\dfrac{3.00\cdot10^8 \ \text{m.s}^{-1} \times 6.626\cdot10^{-34} \ \text{J.s}}{589.9524\cdot10^{-9} \ \text{m}} =3.37\cdot10^{-19} \ \text{J}$

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