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Leto [7]
3 years ago
9

Ultraviolet light emits a total of 2.5 × 10^–17 J of light at a wavelength of 9.8 × 10^–7 m. How many photons does this correspo

nd to?
Physics
1 answer:
tiny-mole [99]3 years ago
6 0
Applying Planck's equation:

E = nhc/λ, with n = number of photons, h = Planck's constant, c = speed of light and λ = wavelength

2.5 x 10⁻¹⁷ = (6.63 x 10⁻³⁴)(3 x 10⁸)n / (9.8 x 10⁻⁷)
n = 123 photons
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Answer:

Energy = 7.83 x 10⁻¹⁹ J

Energy = 6.63 x 10⁻¹⁹ J

Explanation:

The energy of a photon in terms of wavelength can be calculated by the following formula:

Energy = \frac{hc}{\lambda}\\

where,

h = Plank's Constant = 6.63 x 10⁻³⁴ Js

c = speed of light = 3 x 10⁸ m/s

λ = wavelength of light

Now, for λ = 254 nm = 2.54 x 10⁻⁷ m:

Energy = \frac{(6.63\ x\ 10^{-34}\ Js)(3\ x\ 10^8\ m/s)}{2.54\ x\ 10^{-7}\ m}\\

<u>Energy = 7.83 x 10⁻¹⁹ J</u>

<u></u>

Now, for λ = 300 nm = 3 x 10⁻⁷ m:

Energy = \frac{(6.63\ x\ 10^{-34}\ Js)(3\ x\ 10^8\ m/s)}{3\ x\ 10^{-7}\ m}\\

<u>Energy = 6.63 x 10⁻¹⁹ J</u>

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