Answer :
(a) The energy of blue light (in eV) is 2.77 eV
(b) The wavelength of blue light is [tex]4\times 10^{-5}cm[/tex]
Explanation:
The relation between the energy and frequency is:
[tex]Energy=h\times Frequency[/tex]
where,
h = Plank's constant = [tex]6.626\times 10^{-34}J.s[/tex]
Given :
Frequency = [tex]670THz=670\times 10^{12}s^{-1}[/tex]
Conversion used :
[tex]1THz=10^{12}Hz\\1Hz=1s^{-1}\\1THz=10^{12}s^{-1}[/tex]
So,
[tex]Energy=(6.626\times 10^{-34}J.s)\times (670\times 10^{12}s^{-1})[/tex]
[tex]Energy=4.44\times 10^{-19}J[/tex]
Also,
[tex]1J=6.24\times 10^{18}eV[/tex]
So,
[tex]Energy=(4.44\times 10^{-19})\times (6.24\times 10^{18}eV)[/tex]
[tex]Energy=2.77eV[/tex]
The energy of blue light (in eV) is 2.77 eV
The relation between frequency and wavelength is shown below as:
[tex]Frequency=\frac{c}{Wavelength}[/tex]
Where,
c = the speed of light = [tex]3\times 10^8m/s[/tex]
Frequency = [tex]670\times 10^{12}s^{-1}[/tex]
So, Wavelength is:
[tex]670\times 10^{12}s^{-1}=\frac{3\times 10^8m/s}{Wavelength}[/tex]
[tex]Wavelength=\frac{3\times 10^8m/s}{670\times 10^{12}s^{-1}}=4\times 10^{-7}m=4\times 10^{-5}cm[/tex]
Conversion used : [tex]1m=100cm[/tex]
The wavelength of blue light is [tex]4\times 10^{-5}cm[/tex]
