Question

Copper salts are used for fireworks. Copper(II) nitrate has a strong emission at 450nm. Calculate the total energy (in kJ) of the emission for 5.00g. What is the frequency and the color of the light emitted?

Answer 1

Ans. Moles of Cu(NO₃)₂ = Mass / molar mass

= 5.0 g / (187.55588 g/ mol)

= 0.026659 mol

Number of Cu(NO₃)₂ molecules = Number of moles x Avogadro number

= 0.026659 mol x (6.022 x 10²³ molecules/ mole)

= 1.6054 x 10²² molecules.

#a. During transition each Cu(NO₃)₂ molecule emits a photon of 450 nm wavelength.

Energy of the photon is given by-

                        E = hv            - equation 1

; where, h = Plank’s constant = 6.626 x 10^-34 Js   ; v = frequency of photon   

Or, E = h x (c / l)      - equation 2

                        Where, c = speed of light    ; l = wavelength

# Given, the photon has the wavelength of 450 nm.

            Or, wavelength, l = 4.50 x 10^-7 m                           ; [1 nm = 10^-9 m]

Using equation 2, the energy of photon is given by-

E = (6.626 x 10^-34 Js) x (299792458 m s^-1 / 4.50 x 10^-7 m)

            Hence, E = 4.4143 x 10^-19 J

# 1 Cu(NO₃)₂ molecule emits one photon.

So, total number of photons emitted from 5.0 g sample = 1.6054 x 10²² photons

Total energy emission = energy of one photon x total number of photons emitted

                                    = (4.4143 x 10^-19 J/ photon) x 1.6054 x 10²² photons

                                    = 7.0866 x 10³ J

                                    = 7.0866 kJ

#b. Using                   c =v l             - equation 3

            Frequency, v = c / l = (299792458 m s^-1 / 4.50 x 10^-7 m) = 6.6621 x 10¹⁴ s^-1

The color of emitted light (of 450 nm) = violet