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Question
Calculate the energies of the photons associated with the following radiation:
- violet light of 413 nm
- X-rays of 0.1 nm
- radio waves of 10 m
Solution
E = hv
E = `"hc"/λ` in Joule
E = `"hc"/(λe)` in eV
i. violet light of 413 nm
E = `(6.625 xx 10^-34 xx 3 xx 10^8)/(413 xx 10^-9 xx 1.6 xx 10^-19)`
= `19.875/660.8 xx 10^-26 xx 10^28`
= 0.032 × 102
E = 3 eV
ii. X-rays of 0.1 nm
E = `(6.625 xx 10^-34 xx 3 xx 10^8)/(0.1 xx 10^-9 xx 1.6 xx 10^-19)`
= `(19.875 xx 10^-26)/(0.16 xx 10^-28)`
= 124.24 × 102
E = 12424 eV
iii. radio waves of 10 m
E = `(6.625 xx 10^-34 xx 3 xx 10^8)/(10 xx 1.6 xx 10^-19)`
= `19.875/1.6 xx 10^-26 xx 10^-1 xx 10^19`
E = 1.24 × 10−7 eV
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