Question

When sodium is excited in a flame, two ultraviolet spectral lines at lambda - 372.1 nm and lambda = 376.4 nm respectively are emitted . which wavelength represented photons?
 a) higher energy?
b) longer wavelengths?
c) higher frequences?

Answer 1

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:

$E=h\nu =\frac{hc}{\lamda }$ (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.

$\nu$ = 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

$\nu _1=\frac{c}{\lambda _1}=\frac{3\times 10^{8}m/s}{372.1\times 10^{-9} m}=0.08$ 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

$\nu _2=\frac{c}{\lambda _2}=\frac{3\times 10^{8}m/s}{376.4\times 10^{-9} m}=0.07$ Hertz

Answer 2

The wavelength that represented photons is at lambda = 376.4 nm.
The wavelength with the higher energy is at lambda - 372.1 nm.
The longer wavelength is, of course,  at lambda 376.4 nm.
The wavelength with the higher frequency is  376.4 nm.