Question

Consider a photon with a wavelength of 1282 nm. Determine the energy of the photon. (h = 6.626 × 10–34 J⋅s)

Answer 1

The relationship between the energy of a photon (E) and the wavelength of the light (λ) is an inverse relationship and is described by the following by the equation: E=hcλE=hcλ where h is Planck's constant and c is the speed of light

Answer 2

Answer:

$\small \boxed{ \sf \: Energy \: of \: photon \: is \: 1.5514 \times {10}^{ - 19} \: joules}$

Explanation:

Given:

Wavelength (λ) = 1282 nm= 1.282 × 10-⁶ m

planks constant (h) = 6.626 × 10–³⁴ J⋅s

To find:

Energy (E) = ?

Solution:

In Quantum Mechanics the relationship between Energy & wavelength is given

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

Where E is energy in joules

c is speed of light in m/s ( 3 × 10⁸ m/s)

λ is wavelength photon in meter

Substituting the given data & constant values,

$E = \frac{hc}{ \lambda} \\ \\ E = \frac{6.63 \times {10}^{ - 34} \times 3 \times {10}^{8} }{1.282 \times {10}^{ - 6} } \\ \\ E = \frac{19.89}{1.282} \times {10}^{ (- 34 + 8+ 6)} \\ \\ E =15.514 \times {10}^{ - 20} \\ \\ \boxed{\sf E =1.5514 \times {10}^{ - 19} \: joules}$

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