Chemistry: An emission line of sodium has a wavelength of 330 nm. Calculate the energy of a photon of light emitted in J/ atom, and the energy emitted per mole of Na atoms at this wavelength.

Its the hydrogen bonding between hydrogen and oxygen in the water molecule...

An emission line of sodium has a wavelength of 330

glowbaby123

26.01.2022

The energy of the photon of light emitted is $6.024\times 10^{-19}J$ and energy emitted per mole of sodium atoms is $3.63\times 10^{5}J/mol$

Explanation:

The relation between energy and wavelength of light is given by Planck's equation, which is:

$E=\frac{hc}{\lambda}$

where,

E = energy of the photon

h = Planck's constant = $6.626\times 10^{-34}Js$

c = speed of light = $3.0\times 10^8m/s$

$\lambda$ = wavelength of photon = 330 nm = $330\times 10^{-9}m$ (Conversion factor: 1m=10^9nm )

Putting values in above equation, we get:

$E=\frac{6.626\times 10^{-34}Js\times 3.0\times 10^8m/s}{330\times 10^{-9}m}\\\\E=6.024\times 10^{-19}J$

To calculate the energy emitted per mole of sodium atom, we use the equation given by Planck's equation, which is:

$E=\frac{N_Ahc}{\lambda}$

where,

E = energy of the photon

N_A = Avogadro's number = $6.022\times 10^{23}$

h = Planck's constant = $6.626\times 10^{-34}Js$

c = speed of light = $3.0\times 10^8m/s$

$\lambda$ = wavelength of photon = 330 nm = $330\times 10^{-9}m$

Putting values in above equation, we get:

$E=\frac{6.022\times 10^{23}\times 6.626\times 10^{-34}Js\times 3.0\times 10^8m/s}{330\times 10^{-9}m}\\\\E=3.63\times 10^{5}J/mol$

Hence, the energy of the photon of light emitted is $6.024\times 10^{-19}J$ and energy emitted per mole of sodium atoms is $3.63\times 10^{5}J/mol$

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