Question

find the photon energy in eV for electromagnetic wave of wavelength=2271 angstroms (answer= 5.45 eV)​

Answer 1

Given :-

Wavelength, λ = 2271 Å

                        =  2271 × 10⁻¹⁰

To Find :-

Energy of photon in electric volts (eV).

Solution :-

We know :-

$\boxed{ \bf {E = \dfrac{hc}{\lambda} }}$

• E = Energy of photon
• h = Plank's constant ( 6.6 × 10⁻³⁴Js )
• c = Speed of light ( 3 × 10⁸ m/s )
• λ = Wavelength

$:\implies\sf E = \dfrac{6.6 \times {10}^{ - 34} \times 3 \times {10}^{8} }{2271\times {10}^{ - 10}}$

$: \implies \sf E = \dfrac{19.8 \times {10}^{ - 34 + 8} }{2271 \times {10}^{ - 10} }$

$: \implies \sf E = 0.00872 \times {10}^{ -16}$

$: \implies \sf E = 8.72\times {10}^{ - 19 \: } J$

We know :-

$\star \: \bf 1eV = 1.6 \times {10}^{ - 9} J$

∴ Energy of photons in electric volts :-

     $\sf = \dfrac{8.72\times {10}^{ - 19} }{1.6 \times {10}^{ - 19} }$

     $\sf = 5.45 \: eV$

Answer 2

Answer:

Given :-

wavelength = 2271 Å

To Find :-

Photon energy

Solution :-

We know that

E = HC/λ

E = 6.6 × 10⁻³⁴ × 3 × 10⁸/2271 × 10⁻¹⁰

E = (6.6 × 3) × (10⁻³⁴+⁸)/2271 × 10⁻10

E = 19.8 × (10⁻³⁴+⁸)/2271 × 10⁻10

E = 19.8 × 10⁻²⁸/2271 × 10⁻¹⁰

E = 8.72 × 10⁻¹⁹

Now,

In eV

eV = 8.72 × 10⁻¹⁹/1.6 × 10⁻19

eV = 8.72/1.6

eV = 5.4 eV