## Related questions with answers

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

VerifiedSodium’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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