Answer: Wavelength which represented photons with :
a) Higher energy is 372.1 nm
b) Longer wavelength is 376.4 nm
c) Higher frequency is 372.1 nm
Explanation:
\(E=h
u =\frac{hc}{\lamda }\) (Planck's equation)
\(h=\text{Planck's constant}=6.62\times 10^{-34}J-s,c=\text{speed of light}=3\times 10^{8}m/s\)
\(\lambda\) = wavelength of the photon with energy E in meters.
\(u\) = frequency of the photon with energy E in hertz.
For first spectral line:
\(\lambda _1=372.1 nm=372.1\times 10^{-9} m(1nm=1\times 10^{-9} m)\)
\(E_1=\frac{hc}{\lambda_1}=\frac{(6.62\times 10^{-34}J-s)(3\times 10^{8}m/s)}{372.1\times 10^{-9} m}=5.33\times 10^{-19}\) joules
\(u _1=\frac{c}{\lambda _1}=\frac{3\times 10^{8}m/s}{372.1\times 10^{-9} m}=0.08\) Hertz
For second spectral line:
\(\lambda _2=376.4 nm=376.4\times 10^{-9} m(1nm=1\times 10^{-9} m)\)
\(E_2=\frac{hc}{\lambda_2}=\frac{(6.62\times 10^{-34}J-s)(3\times 10^{8}m/s)}{376.4\times 10^{-9} m}=5.27\times 10^{-19}\) joules
\(u _2=\frac{c}{\lambda _2}=\frac{3\times 10^{8}m/s}{376.4\times 10^{-9} m}=0.07\) Hertz
