Respuesta :
Answer : The energy and frequency of yellow and blue peak is, 2.10 eV, [tex]5.09\times 10^{14}Hz[/tex] and 2.84 eV, [tex]6.88\times 10^{14}Hz[/tex] respectively.
Explanation :
Part 1:
Given:
Wavelength of yellow peak = [tex]589nm=589\times 10^{-9}m[/tex]
Conversion used : [tex]1nm=10^{-9}m[/tex]
First we have to calculate the frequency of yellow peak.
Formula used :
[tex]\nu=\frac{c}{\lambda}[/tex]
where,
[tex]\nu[/tex] = frequency of yellow peak
[tex]\lambda[/tex] = wavelength of yellow peak
c = speed of light = [tex]3\times 10^8m/s[/tex]
Now put all the given values in the above formula, we get:
[tex]\nu=\frac{3\times 10^8m/s}{589\times 10^{-9}m}[/tex]
[tex]\nu=5.09\times 10^{14}s^{-1}=5.09\times 10^{14}Hz[/tex] [tex](1Hz=1s^{-1})[/tex]
The frequency of yellow peak is, [tex]5.09\times 10^{14}Hz[/tex]
Now we have to calculate the energy of yellow peak.
Formula used :
[tex]E=h\times \nu[/tex]
where,
[tex]\nu[/tex] = frequency of yellow peak
h = Planck's constant = [tex]6.626\times 10^{-34}Js[/tex]
Now put all the given values in the above formula, we get:
[tex]E=(6.626\times 10^{-34}Js)\times (5.09\times 10^{14}s^{-1})[/tex]
[tex]E=3.37\times 10^{-19}J[/tex]
Also,
[tex]1J=6.24\times 10^{18}eV[/tex]
So,
[tex]Energy=(3.37\times 10^{-19})\times (6.24\times 10^{18}eV)[/tex]
[tex]Energy=2.10eV[/tex]
The energy of yellow peak is [tex]2.10eV[/tex]
Part 2:
Given:
Wavelength of blue peak = [tex]436nm=436\times 10^{-9}m[/tex]
Conversion used : [tex]1nm=10^{-9}m[/tex]
First we have to calculate the frequency of blue peak.
Formula used :
[tex]\nu=\frac{c}{\lambda}[/tex]
where,
[tex]\nu[/tex] = frequency of blue peak
[tex]\lambda[/tex] = wavelength of blue peak
c = speed of light = [tex]3\times 10^8m/s[/tex]
Now put all the given values in the above formula, we get:
[tex]\nu=\frac{3\times 10^8m/s}{436\times 10^{-9}m}[/tex]
[tex]\nu=6.88\times 10^{14}s^{-1}=6.88\times 10^{14}Hz[/tex] [tex](1Hz=1s^{-1})[/tex]
The frequency of blue peak is, [tex]6.88\times 10^{14}Hz[/tex]
Now we have to calculate the energy of blue peak.
Formula used :
[tex]E=h\times \nu[/tex]
where,
[tex]\nu[/tex] = frequency of blue peak
h = Planck's constant = [tex]6.626\times 10^{-34}Js[/tex]
Now put all the given values in the above formula, we get:
[tex]E=(6.626\times 10^{-34}Js)\times (6.88\times 10^{14}s^{-1})[/tex]
[tex]E=4.56\times 10^{-19}J[/tex]
Also,
[tex]1J=6.24\times 10^{18}eV[/tex]
So,
[tex]Energy=(4.56\times 10^{-19})\times (6.24\times 10^{18}eV)[/tex]
[tex]Energy=2.84eV[/tex]
The energy of blue peak is [tex]2.84eV[/tex]
