a) The emission line with the longest wavelength. 5
b) The absorption line with the shortest wavelength. 3
c) The emission line with the highest energy. 4
d) The absorption line with the lowest energy. 1
e) The emission line with the lowest frequency. 5
f) The line corresponding to the ionization energy of hydrogen. 3
Explanation:
To answer this questions we need to take in account the following:
Formula for photon (light) energy is:
E = h × c / λ
where:
E - energy
h - Planck constant
c - speed of light
λ - wavelength of light
And if you talk about frequency:
E = c × f
where:
E - energy
c - speed of light
f - frequency
So from this equations (taking in account that h and c are constants) we deduce that:
Light with high energy have a short wavelength and a high frequency.
Light with low energy have a long wavelength and a low frequency.
a) The emission line with the longest wavelength. 5
For the emission line number 5 the electrons will decay from the n=2 level to n=1 level with emission of photons. This emission it is lower in energy that the line 4 which corresponds to a higher energy photon emission.
The emission line number 5 is have the lowest energy so it will have the longest wavelength.
b) The absorption line with the shortest wavelength. 3
The hydrogen will absorb energy promoting an electron from the ground energy level, n=1, to a higher energy level. The higher the energy level required for the promotion the shortest the wavelength of light needed to be absorbed.
c) The emission line with the highest energy. 4
The electron will decay from the energy level n=4 on the ground level with n=1. Fromm the diagram you may see that it have the highest energy.
d) The absorption line with the lowest energy. 1
The hydrogen absorb energy promoting an electron from the ground energy level, n=1, to the energy level with n = 2. You may see from the diagram that this absorption line have the lowest energy.
e) The emission line with the lowest frequency. 5
The emission line with the lowest frequency is the emission line with the lowest energy, which is 5.
f) The line corresponding to the ionization energy of hydrogen. 3
The absorption line 3 correspond to the promotion of an electron of hydrogen from the ground level to infinity which means that the electron is removed from the hydrogen atom thus obtaining the ionized hydrogen.
Learn more about:
emission spectrum
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