What is the wavelength, in nm, of a photon with energy 0.30 eV? Express your ans

Question

What is the wavelength, in nm, of a photon with energy 0.30 eV? Express your answer using two significant figures. Is this wavelength visible, ultraviolet, or infrared light? visible light Ultraviolet light infrared light What is the wavelength, in nm, of a photon with energy 3.0 eV? Express your answer using two significant figures. Is this wavelength visible, ultraviolet, or infrared light? visible light Ultraviolet light infrared light What is the wavelength, in nm, of a photon with energy 30 eV? Express your answer using two significant figures.

Explanation / Answer

Given, energy E=.3eV=0.3*1.6*10(^-19)=4.8*10^(-20) J

OR, 4.8*10^(-20) J = Planck's constant * frequency

OR, 4.8*10^(-20) J = 6.626*10^(-34) J-s * frequency

OR, frequency = 7.244*10^13 Hz.

So, wavelength= speed of photon/frequency = 3*10^8 / 7.244*10^13 =4.1413* 10^(-6) m OR 4141.3 nm. (A)

700nm-1mm is wavelength for infrared radiation. Hence it is infrared light. (B)

Similarly, for E=3eV=48*10^(-20) J

= Planck's constant * frequency

OR,48*10^(-20) J = 6.626*10^(-34) J-s * frequency

OR, frequency= 72.44*10^13 Hz

So, wavelength = 3*10^8 / 72.44*10^13 = 414.13 nm. (C)

400-700 nm is visible light. So 414 nm is visible light. (D)

similarly, for E=30eV=480.6*10^(-20) J

OR, 480.6*10^(-20) J = 6.626*10^(-34) J-s * frequency

OR, Frequency= 724.4*10^13 Hz

OR, wavelength =3*10^8 / 724.4*10^13 = 41.413 nm. (E)

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