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Question
The energy of a photon is 2 eV. Find its frequency and wavelength.
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Solution
Given:
E = 2 eV = 2 × 1.6 × 10−19 = 3.2 × 10−19 J
To find:
- Frequency (ν)
- Wavelength (λ)
Formulae:
- E = hν
- λ = `c/ν`
Calculation:
i. Using formula (i),
v = `(3.2 xx 10^-19)/(6.63 xx 10^-34)`
= `(3.2 xx 10^15)/6.63`
= antilog {log (3.2) + log(1015) − log(6.63)}
= antilog {0.5051 + 15 − 0.8215}
= antilog {14.6836}
= 4.826 × 1014 Hz
The frequency of photons is 4.826 × 1014 Hz.
ii. Using formula (ii),
`λ = c/ν = (3 xx 10^8)/(4.826 xx 10^14)`
= antilog {log 3 − log 4.826} × 10−6
= antilog {0.4771 − 0.6836} × 10−6
= antilog {`overline1`.7935} × 10−6
= 0.6216 × 10−6m
= 6216 × 10−5 m
= 6216 Å
The wavelength of the photon is 6216 Å.
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