Question

The element vanadium had a line with a wavelength of 318.5 nm in its emission spectrum. What is the frequency of this line

Answer 1

The frequency of this line of vanadium  is 9.38 x10 ^14 Hz.

Emission spectrum shows how the electron of an atom goes or moves  from a higher to a lower energy level.

Now The energy of a photon is given by

E = hc/λ

where  

h = Plank's constant =  6.626 x 10⁻³⁴ J s

c = speed of light=   3 x 10⁸ m/s

λ = wavelength =  318.5  x 10⁻⁹ m  

Solving

E =  (6.626 x 10⁻³⁴ J s x 3 x 10⁸ m/s)  / 318.5  x 10⁻⁹ m

E =6.2166 x10 ^-19 J

Also, we know that energy is related to frequency by the equation

E =hf

Where;

h = Planks's constant

f = frequency of photon

Making frequency subject of the formulae

f = E/h

f =6.2166 x10 ^-19 J/  6.626 x 10⁻³⁴ J s

f =  9.38 x10 ^14 Hz

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