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The energy of a photon having wavelength 100 Å will be -
1. 16 × 10-24 J
2. 23 × 10-21 J
3. 5.3 × 10-15 J
4. 2.0 × 10-17 J

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Correct Answer - Option 4 : 2.0 × 10-17 J

Concept:

Photon

  • A photon is a packet of energy that forms light. 
  • Each photon has energy E = h ν where ν is the frequency of the wave, h is Planck's constant. 
  • The energy can also be represented as 

\(E = h\frac{c}{λ }\)

where λ is the wavelength, c is the speed of light,

c = 3 × 10 8 m /s 

Calculation:

Given, 

Wavelength λ = 100 Å

1  Å = 10 -10 m

So, wavelength in meter

λ = 100 Å = 10 2 × 10 -10 = 10 -8 m

The energy can also be represented as 

\(E = h\frac{c}{λ }\)

\(\implies E = (6.626 × 10 ^{-34})\frac{3 × 10^8}{10^{-8} } J\)

⇒ E = 19.878 × 10 (-34 + 8 + 8 ) J = 19.878 × 10 - 18 Joule

 ⇒ E ≈ 2.0 × 10-17 Joule

So, the correct option is 2.0 × 10-17 J

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